GM CEO Mary Barra recently met with the newest candidate for a seat on GM's board Harry J. Wilson.

A group of four heavyweight hedge funds that controls 2.1% of the General Motors’ shares wants a seat on the automaker’s board of directors and a change in company policy requiring a steep increase in share buy backs.

Harry J. Wilson is a corporate turnaround expert, who is a former member of President Obama’s Auto Task Force and a failed political candidate from New York, submitted a letter to the automaker saying he plans to seek election to the board during the company’s annual shareholder meeting.

The company is treating his candidacy with kid gloves, issuing a statement saying the company is “evaluating” the proposal. Acting on behalf of the four funds, Wilson is pushing a plan to require the automaker to buy back as much as $8 billion of its outstanding shares. He has a substantial incentive to get the measure adopted.

“Mr. Wilson’s notice further indicates a fee arrangement under which he will receive a percentage of the group’s profits from their investment in GM,” the letter said.

Wilson, who is currently a director of Yahoo, lost a bid to become the comptroller of the state of New York in 2010.

During the years, GM’s practice has been to reject proposals from outside groups and activist or dissident shareholders. However, GM also disclosed that Wilson met last week with GM Chief Executive Officer Mary Barra, indicating that the automaker believed it could not dismiss the proposal out of hand.

Wilson’s buy back proposal would put heavy pressure on the company’s financial reserves at a time when its European operations are still losing money, it’s continuing to invest major resources in China and it’s caught up in intense product competition in the United States where driverless cars are threatening to disrupt its traditional business.

The four investment funds that support his election and proposal include Taconic Parties, Appaloosa Parties, HG Vora Parties and the Hayman Parties, which together own approximately 34.4 million shares of the company’s common stock.

GM said Wilson first informed the company of his interest in being nominated to GM’s Board of Directors at a meeting with Barra on Feb. 3, a meeting requested by Wilson “for other purposes.”

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He disclosed the identity of the members of his group for the first time in his notice, submitted just before the deadline of midnight, Feb. 9. GM has had regular contact with some of the investors identified in the group, including as recently as after its earnings announcement on Feb. 4, and at no time in discussions with GM have they indicated an interest or intent to nominate directors to the GM board.

The Board’s Directors and Corporate Governance Committee will evaluate the proposed director nominee based on the criteria set forth in the company’s Corporate Governance Principles and Director Qualification Standards and make a recommendation based on the best interests of all shareholders. GM shareholders are not required to take any action at this time.

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GM, perhaps anticipating the pressure from activist investors, also recently announced plans for 20% increase of the quarterly dividend to 36 cents per share to be declared as part of the board’s regularly scheduled second quarter 2015 common stock dividend declaration process.

However, there has been some speculation that the company may need to do more than just up the dividend to keep investors happy. In a note Tuesday, Barclays Capital Inc. analyst Brian A. Johnson, said that despite upcoming issues like recall lawsuits and UAW negotiations, GM might initiate a share buy back.

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“We believe there is a fair likelihood that GM enacts some sort of share buy back (perhaps $4 billion) to show investors that it is enhancing shareholder value,” he said.