Republic Airways Holdings Inc. agreed to seek new investors for Frontier Airlines, shrinking its stake to become a minority owner, in exchange for concessions from pilots at the unprofitable carrier.

The agreement is part of a plan to cut Frontier’s operating costs by $100 million, Indianapolis-based Republic said Friday in a federal regulatory filing. Republic, which bought Frontier out of bankruptcy in 2009, would reduce its holdings to less than a majority by the end of 2014.

Republic has struggled to mesh its primary business, operating regional flights for carriers such as Delta Air Lines Inc. and United Continental Holdings Inc., with the regularly scheduled passenger flights at Frontier.

Shares of Republic reached a 52-week low last week, closing Friday at $4.21.

Republic outbid much bigger rival Southwest Airlines to buy Frontier in a rare defeat for the Dallas-based carrier, which has been gunning hard against Frontier in key markets such as Denver.

Before buying Frontier—along with Milwaukee-based scheduled carrier Midwest Airlines in 2009—Republic since the 1970s had exclusively flown smaller, regional jets on contract for scheduled carriers.

Contract flying is not as vulnerable to spiking jet-fuel costs, as the brunt of such expenses are borne by the scheduled carrier that hires Republic. The contract flying unit produces “reasonably predictable margins” in the 7.5-percent to 8.5-percent range, Republic executives told analysts recently.

But Frontier’s fuel expenses during the first quarter of 2011 were 24 percent higher than the same period in 2010, representing a $30 million increase.  Republic recently said it is projecting further rises in fuel prices for the last three quarters of this year, or about a $90 million increase in expenses.

Republic’s acquisitions also created one of the industry’s most complicated labor integration challenges, particularly among pilots. Republic’s 2,500 pilots are represented by three unions, four counting the 400 Air Line Pilots Association-represented Midwest pilots that were placed on on furlough.

The pilot accord includes postponing scheduled pay increases; paring company contributions to a 401(k) plan; reducing sick days and vacation time; and extending the current labor contract by two years. It must be approved by pilots and Republic’s board.

Pilots would receive an equity stake in Frontier in exchange, according to the filing.

Republic must make a “good-faith” effort to find new investors and cut its ownership, raise at least $70 million through issuing debt or other financings, boost the size of Frontier’s fleet, establish a profit-sharing program for Frontier workers and implement a restructuring plan by the end of this year, according to the filing.