While it failed to name the ways specific corporations avoided taxes, the GAO survey, based on Internal Revenue Service records, attributes the failure to three factors: tax credits, operating losses and “transfer pricing,” which means corporations internally shift taxable profits to their own subsidiaries in lower-tax nations.
Transfer pricing means a corporation “sells” its products to a subsidiary in another country at a low profit. They pay taxes on that low profit. The subsidiary then sells the product at full price.
The GAO report (PDF) has much more about how corporations avoid taxes.