With a Senate panel about to examine how Apple sidestepped tens of billions of dollars in taxes around the world, a showdown may be shaping up.

In one corner is Senator Carl Levin, the Michigan Democrat who is chairman of the Senate’s Permanent Subcommittee on Investigations and a fierce critic of what he sees as corporate wrongdoing. His recent tangles with JPMorgan Chase and Goldman Sachs left executives licking their wounds, but in Apple’s chief executive, Timothy D. Cook, he faces a different kind of adversary.

Unlike those Wall Street giants, Apple is beloved by legions of consumers, and the company plans to make its case that current tax law is out of step in the global digital economy. Mr. Cook, a 15-year Apple veteran who took over as chief executive in 2011 from Steven P. Jobs, has a keen knowledge of Apple’s operations, and will be joined by two top aides: Peter Oppenheimer, the company’s chief financial officer, and Phillip A. Bullock, its head of tax operations.

Before they testify, however, the panel will hear from two academic experts on tax policy, Stephen E. Shay of Harvard Law School and J. Richard Harvey from the Villanova University School of Law. The hearings, which are likely to stretch on for hours, will conclude with the appearance of two senior officials from the Internal Revenue Service, Samuel M. Maruca and Mark J. Mazur. Live video of the hearing is available at NBCNews.com

11:19 A.M. The Fairness of Apple’s Practices

Senator McCain asked the two professors whether, by taking a tax deduction in a country in which Apple “has no employees,” Apple has put other companies at a disadvantage. The two professors said it certainly has.

And Professor Shay added that the global tax system wa out of balance. Most of the creative work on Apple products is done in the United States but a proportionate amount of tax revenue, he said, is not flowing into the Treasury’s coffers.

â€" Jeff Sommer

11:15 A.M. Opinions on Recommendations of Simpson-Bowles

Senator Tom Carper, Democrat of Wisconsin, asked the tax experts to give their opinion on the recommendations of the Simpson-Bowles commission on tax reform.

Professor Shay said the “realism of eliminating all tax expenditures is somewhat overstated; I don’t think it’s going to happen.”

He said “we need more revenues” from taxes. Professor Shay, a former Treasury official in the Reagan administration, said that making significant changes in the tax code is likely to take “considerable time.”

Professor Harvey added that he would emphasize that it’s crucial to avoid tax “base erosion,” in which taxpayers, presumably like Apple, find ways of circumventing the tax code.

â€" Jeff Sommer

11:10 A.M. Question on Leeway for Multinationals

Professor Harvey said, “When you have 64 percent of your income in a country like Ireland” with no employees there and minimal sales, there’s a serious problem. “Are you going to let us multinationals effectively have full rein to move all their earnings offshore?”

These are difficult issues, he said, but Congress needs to face up to them.

Meanwhile, my colleague Nelson Schwartz reports from the hearing room that Tim Cook, Apple’s chief executive, has arrived and taken his seat in the witness section with an entourage from Apple.

â€" Jeff Sommer

10:56 A.M. A View on Apple’s Cost-Sharing

Professor Shay says that viewing Apple’s cost-sharing with its subsidiaries as anything other than tax avoidance strains credulity.

“There are bad deals out there,” he said. “This would be a whopper. A whopper against Apple.”

This deal was not an arms-length transaction between independent companies, he suggested. Consider this, he said: “Would you still own the stock if somebody gave away that much income?” The answer, he implied, was clearly no, but the deal makes sense because of its tax implications.

â€" Jeff Sommer

10:51 A.M. Rethinking Rules for Digital Economy

“We talk about globalization,” Professor Shay said. “We are aware that we have a digital economy. We have ways of earning income that no longer have a physical nexus” to a specific country. “It is import to rethink our rules,” he said.

â€" Jeff Sommer

10:46 A.M. Professor Shay’s Recommendation

Professor Shay says Congress shouldn’t wait for major systemic tax reform before addressing “income shifting” of the kind highlighted by the committee. And he applauds the committee for bringing to light international tax practices “that are not easily understood.”

â€" Jeff Sommer

10:42 A.M. Professor Shay on Location of Apple’s Income

Professor Shay said the average effective book tax rate for Apple’s Irish companies was well below 1 percent. Although Apple has listed their “location for tax purposes as Ireland,” he said, he learned for the first time on Sunday night that two of Apple’s subsidiaries, Apple Operations Europe and Apple Sales International, actually “are not tax residents in Ireland.”

“It’s not clear” where taxes on most of their income is paid, he said. Their income is being designated as belonging nowhere. It appears, he said, to be what is “oddly referred to by international tax planners as ‘ocean income.’”

10:41 A.M. Discussion of Possible Long-Term Solutions

Professor Harvey raises possible long-term solutions, and says he does not recommend that the United States adopt a worldwide tax system unless it reduces its corporate rate to 15 percent, which he says he thinks is not likely. If the current system allowing “transfer-pricing” is retained, he said, it needs to be clearer and made more easily administrated. And he relinquishes the floor to Professor Shay of Harvard.

â€" Jeff Sommer

10:37 A.M. Tax Loopholes as Magic

Professor Harvey discussed various tax loopholes, including “check-the-box tax rules.” One of his children is an aficionado of magic tricks, he said. Using his son’s language, he said, “check-the-box” is a technique that enables Apple to “make its taxes go poof.”

â€" Jeff Sommer

10:29 A.M. Professor on Apple’s ‘Tax Gimmicks’

In 2011, Professor Harvey said, Apple allocated $ 22 billion in profit to Apple Sales International in Ireland, which enabled Apple to “accomplish a .05 percent tax rate.”

He said that he would digress for a moment to rebut Apple’s prepared testimony, which includes the assertion that “Apple does not use tax gimmicks.”

When he read that, he said, “I just about fell off my chair.” Any reasonable person would conclude that these are tax gimmicks, he said.

â€" Jeff Sommer

10:26 A.M. Witnesses Begin Testimony

Senator Levin has introduced two academic experts, Stephen E. Shay of Harvard Law School and J. Richard Harvey of Villanova University School of Law. Professor Harvey has started his testimony on transfer pricing and shifting of profits by multinationals offshore, and on Apple’s specific tax planning techniques.

Apple, he said, was able to allocate 64 percent of its income to Ireland, which, he said, is “really an entity only on paper.” He said that Apple “isn’t as aggressive as others.” What is “scary,” he said, is that many companies would have gone even further. He questions whether the current global system that allows such tax avoidance makes any sense.

â€" Jeff Sommer

10:21 A.M. A Proposal From Senator Paul

Senator Paul said he had proposed a bill to tax repatriated capital held overseas by American company at 5 percent, instead of at the statutory rate of 35 percent. Companies like Apple would then bring their cash back home, he said. (Apple has more than $ 100 billion in “offshore” cash, the company acknowledges.)

The returned cash would go into a fund for infrastructure reconstruction, he said, and then he returned the floor to Senator Levin.

â€" Jeff Sommer

10:20 A.M. A Sharply Different Take From Rand Paul

Senator Rand Paul, the Kentucky Republican, has taken the floor with a very different tone. He says he is “offended” by the hearings. Who, he said, doesn’t try to minimize their own taxes?

“Tell me what Apple has done that’s illegal,” he said.

He said he’s offended by an I.R.S. that bullies the Tea Party, and that he’s offended by a government that is trying to “bully” a great company, and called the hearing “a show trial.”

He continued along these lines on Twitter:

â€" Jeff Sommer

10:15 A.M. McCain on Irish Subsidiaries

From 2009 to 2012, Apple Operations International in Ireland received $ 30 billion in dividend income from other Apple subsidiaries around the world, Mr. McCain said. While the company held tens of billions of dollars in cash it appeared to have no employees.

He said that 95 percent of Apple’s research and development takes place in the United States. Less than 1 percent of it takes place in Ireland. And, he said, Apple’s Irish subsidiaries are a “tax resident nowhere in the world,” a nebulous legal status that allows the parent company to avoid taxes globally.

Senator McCain has concluded his statement.

â€" Jeff Sommer

10:07 A.M. Levin Calls for Crackdown on Loopholes

While Apple says it paid $ 6 billion in federal taxes in 2012, Mr. Levin said, it also avoided $ 9 billion in United States taxes that year. That, he said, amounts to $ 25 million a day, or more than $ 1 million an hour.

After calling for a crackdown on tax loopholes, he gave the floor to Senator John McCain, Republican from Arizona, who also began his presentation by saying how much he admired Apple as a creator of great products. Senator McCain decried what he described as Apple’s “scheme” to avoid taxes.

â€" Jeff Sommer

10:04 A.M. A Comparison With Apple’s U.S. Earnings

Senator Levin compares Apple’s earnings in the United States with its earning through its Irish subsidiaries. From 2009 to 2012, Apple Inc. in the United States paid $ 4 billion and declared profits of $ 38 billion. In other words, he said, its Irish subsidiary received almost twice the profits that its parent did from intellectual property developed by Apple in the United States.

“It’s hard to imagine Apple offering such a deal at any price” to an outside company, Mr. Levin said.

â€" Jeff Sommer

10:00 A.M. Almost $ 70 Billion in Missed Taxable Income

Figures provided by Apple over a four-year period, from 2009 to 2012, show that one Irish subsidiary paid approximately $ 5 billion to the parent company in the United States as the subsidiary’s share of research and development costs, Senator Levin said. During that period, the subsidiary received profits of $ 74 billion. The difference, almost $ 70 billion, is how much taxable income would have otherwise flowed to the United States, he said.

â€" Jeff Sommer

9:57 A.M. Other Common Tax Avoidance Strategies

Mr. Levin has moved on to other tax avoidance strategies. He focuses on one that he said is more common among United States companies. That is “transfer pricing,” under which a company shifts intellectual property abroad, allowing it to shift taxable income to low-tax havens.

“Apple set up its cost-sharing agreements with its Irish subsidiaries,” he said. He added: “I use the term ‘cost-sharing’ with some skepticism,” because ultimately it is about shifting profits away from the United States and “instead concentrating the lion’s share of profits from most of the world to Apple’s subsidiaries in Ireland.”

â€" Jeff Sommer

9:54 A.M. Apple Exploits an Absurdity, Levin Says

“Apple is exploiting an absurdity, one that we have not seen other companies use,” Senator Levin said.

But he added that this situation need not continue. “It is possible to penetrate an entity’s corporate structure for tax purposes and to collect U.S. taxes on its income,” he said. This can be done by showing that a part of the company created to avoid taxes is “nothing more than instrumentality of its parent company, a sham.”

Three of Apple’s subsidiaries “sure seem to fit that description,” he said.

â€" Jeff Sommer

9:50 A.M. Levin on Apple’s Corporations in Ireland

Apple has created corporations in Ireland that enable it to avoid United States taxes, Senator Levin said. Apple Operations International is one of them. It is incorporated in Ireland. But, he said, “Magically it is neither here nor there,” as far as taxes are concerned.

â€" Jeff Sommer

9:47 A.M. Professor Says Cost-Sharing Deals Saved Apple Billions

In his opening testimony, J. Richard Harvey Jr., a professor at Villanova Law School, estimates that cost-sharing agreements alone saved the company $ 7.7 billion in potential American taxes in 2011.

“Apple is an iconic U.S. multinational corporation that has enjoyed extraordinary financial success,” he will tell the committee, according to prepared testimony. “In addition to demonstrating excellence in designing, building and selling consumer products, Apple has been very successful at minimizing its global income tax burden.”

In 2011, 64 percent of Apple’s global pretax income was recorded in Ireland, where only 4 percent of its employees and 1 percent of its customers are located, according to Professor Harvey.

â€" Nelson D. Schwartz

Senator Carl Levin, chairman of the subcommittee, begins the hearing by saying that like millions of other Americans, he uses Apple products like an iPhone. But, he said, Apple is seeking “the holy grail of tax avoidance” with tax strategies that are unique.

â€" Jeff Sommer