Google has sued the Internal Revenue Service over a stock transaction dating back to 2004 with America Online.

The company filed the complaint in U.S. tax court on Thursday, claiming that the U.S. government owes the search giant $83.5 million. Bloomberg, which was first to report the news, spoke with a Google spokeswoman who said that the company hopes "to have it resolved soon."

Google argues that the IRS erroneously disallowed a $238.6 million deduction the company took related to the difference in value between what AOL paid to exercise a Google stock warrant and the actual value of the company's shares.

A stock warrant gives the holder -- in this case, AOL -- the right to purchase shares at a previously set price within a certain time frame. According to the suit, AOL acquired the $238.6 million in shares about three months before Google priced its IPO and went public. That effectively left Google without those shares to sell in its IPO, and since the warrants were used as remuneration for services AOL was providing to Google at the time, the company wanted to expense the total share outlay.

It's not clear when the case will be heard by the tax court.