American International Group, the huge insurance company under investigation by state and federal regulators over accounting issues, filed its long-awaited 2004 annual report with the SEC yesterday, restating financial results for the past five years.

As part of the restatement, AIG cut shareholders’ equity at December 31, 2004,by $2.26 billion, or 2.7%,to $80.61 billion, less than the $2.7 billion reduction the company had projected earlier. This included an after-tax reduction of $1.19 billion for changes in estimates for the fourth quarter of 2004.

In revised calculations, the New York-based company lowered profits by nearly $4 billion for the five years since 2000. The biggest of those changes came in 2004, with net income cut by $1.32 billion, or nearly 12%, to $9.73 billion from the $11.05 billion that had been reported February 9.

In its new filing with the SEC, AIG acknowledged accounting improprieties, including “improper or inappropriate transactions.”

It also said: “In many cases, these transactions or entries appear to have had the purpose of achieving an accounting result that would enhance measures believed to be important to the financial community and may have involved documentation that did not accurately reflect the true nature of the arrangements.”

In some instances, the filing said, the transactions “may also have involved misrepresentations to members of management, regulators and AIG’s independent auditors.”