Tthe Civil Aeronautics Board yesterday began the process of seriously considering the application of World Airways to offer scheduled coast-to-coast air service for about half the current cross-country fares.

Should the board eventually approve World's proposal, the action could have a far-reaching impact on U.S. airline regulation, possibly forcing an alteration in the CAB's complicated fare-setting framework if other carriers - as would be expected - sought to meet World's price.

In another action which could yield consumer benefits if successful, the Aviation Consumer Action Project sued the CAB and its members, charging that they had been derelict in their duties in not acting to upgrade the airlines' responsibilities for lost or damaged baggage.

The board acted on the World application - setting it for hearing before an administrative law judge - after the United States Court of Appeals for the District of Columbia held that, under the Federal Aviation Act, the board can grant a charter airline the authority also to offer scheduled air service. The board previously had held that it did not have such power, and had dismissed World's 1975 application a year ago on those grounds.

World, which holds a federal certificate to offer charter air service, had asked for authority to offer scheduled cross-country flights from Baltimore and Newark to Oakland and Ontario, Calif., for $89 each way.

Because of increased costs since the application was filed, it's believed that World may want to raise the proposed fare somewhat, perhaps up to $100. Air fare over the same distances is now nearly double; a one-way coach ticket from Washington to Los Angeles, for instance, is $192 and will go to $196 in February with the recently approved fare increase.

World had filed a similar application in 1967 seeking authority to offer scheduled air service across the country for $75 each way. The application languished as the board refused to grant a hearing on it; six and one-half years later, the application was dismissed as stale.

The board yesterday said that, in the World case, it would follow similar procedures to those it has outlined for the consideration of the applications of two corporations to offer low-cost flights in and out of Chicago's Midway Airport.

The board will receive comments from interested parties before it defines the precise scope of the proceeding and designates the route and rate issues to be resolved, including the relationships of World's fare proposal to the requirements of the board's rate-setting standards.

In its suit filed in U.S. District Court here yesterday, ACAP, a Ralph Nader-connected non-profit organization, accused the CAB of failing to meet its obligation to assure the justness and reasonableness of airline rules and practices affecting passengers by failing to reform its baggage rules.

In the sumer of 1973, ACAP had filed a petition seeking such a change. Under rules adopted in 1966, the airlines are permitted to limit their liability for loss or damaged baggage to a recovery of $500 a person regardless of the number of bags lost or what was in them.

". . . it is obvious that the monetary limits on baggage liability set over a decade ago have become wholly inadequate because of inflation," Patricia Kennedy, ACAP's associate director, said yesterday.

Almost two years ago, the board tentatively concluded that the liability was too low and issued an order seeking information on why it shouldn't raise the level to a minimum of $750. Since that time, however, it has taken no action.