CRJ200 FLT CREW HAS A RWY INCURSION AT LGA.

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THIS EVENT OCCURRED WHILE TAXIING AT LGA. THE ACFT AND CREW GOT IN LINE TO TAXI BEHIND A B717 ON TXWY B AND TXWY L. WE WERE INSTRUCTED TO FOLLOW THE B717 ON TXWY B TO TXWY F AND HOLD SHORT OF RWY 22 AT TXWY F. THERE WERE 20-25 ACFT TAXIING OUT AT THIS TIME. GND CTL HAD NUMEROUS ACFT SITTING ON TXWY AA; TXWY CC; AND TXWY Y AWAITING RELEASE TIMES. PRIOR TO US XING RWY 22; GND TWICE GAVE US TAXI INSTRUCTIONS MEANT FOR ANOTHER ACR ACFT. THE B717 WAS CLRED ACROSS RWY 22 AT TXWY F; TO GO L ON TXWY AA; R ON TXWY D; R ON TXWY BB; R ON TXWY F AND FOLLOW ANOTHER ACFT FACING TXWY E ON TXWY AA. SEVERAL MINS PASSED AND WE WERE CLRED ACROSS RWY 22 WITH WHAT WE THOUGHT WERE THE SAME INSTRUCTIONS AS THE B717 (AT THIS MOMENT; I DO NOT REMEMBER WHAT WAS INSTRUCTED; OR WHAT I READ BACK). WE STARTED ACROSS RWY 22 ON TXWY F. ABOUT 1/2 WAY ACROSS WE REALIZED THERE WAS NO ROOM ON TXWY F ON THE OTHER SIDE; AS THE B717 AND THE ACFT ON TXWY AA HAD TAKEN UP MORE SPACE THAN WAS APPARENT BEFORE WE STARTED ACROSS RWY 22. WE THEN TURNED L ON RWY 22 AND WENT DOWN TO TXWY D AND EXITED R. WHILE ON THE RWY; GND BEGAN TO ASK WHAT WE WERE DOING; BUT STOPPED AND TOLD US TO EXIT AT TXWY D; TURN R ON TXWY AA. IN THE BACKGND OF HIS OPEN MIKE; I HEARD THE TWR CTLR ASK; 'WHERE ARE THEY GOING?' THEN DIRECT AN ACFT ON FINAL TO GO AROUND DUE TO AN ACFT ON THE RWY. ONCE WE CLRED ONTO TXWY AA; GND DIRECTED US TO FOLLOW THE B717; WHICH WE DID; FOR AN UNEVENTFUL FLT. NEITHER GND NOR TWR COMMENTED ABOUT THE INCIDENT ONCE WE WERE CLR OF RWY 22.