GA SMA UNAUTHORIZED RWY XING CAUSES UNKNOWN TO GAR.

Narrative

I WAS CLRED TO LAND BY PNE TWR ON ILS RWY 24. I TOLD THE TWR PRIOR TO TOUCHING DOWN THAT I WOULD BE GOING TO THE FBO WHICH I BELIEVE SHE ACKNOWLEDGED. I GAVE HER THIS INFO ANTICIPATING A HDOF TO THE GND CTLR UPON TURNING OFF THE RWY. I LANDED ON RWY 24 WITH NO PROBLEM. I TURNED OFF TO THE R ON THE NEXT AVAILABLE TAXIWAY A. SINCE I'M FAMILIAR WITH THE ARPT; I MADE THE NEXT R ON THE TAXIWAY LIMA. I STILL WAS NOT CONTACTED BY THE TWR TO GO OVER TO THE GND FREQ SO I CONTINUED TO TAXI ON TAXIWAY LIMA XING RWY 15/33. OFF MY L I SAW AN ACFT ON SHORT FINAL AND I SPED UP OFF RWY 15/33. THE TWR REALIZED WHAT HAPPENED AND THE PLT OF THE LNDG ACFT SAW ME (I HAD STROBES; BEACON; NAV LIGHTS; TAXI LIGHT ON) AND DID A GAR. I WAS TOLD BY THE TWR TO BE MORE CAREFUL; AND I TAXIED TO THE FBO WITHOUT INCIDENT. IN RETROSPECT; I WAS NOT AWARE I HAD CROSSED 15/33 ON RWY 6/24 SO WHEN I TAXIED BACK; I WASN'T LOOKING TO CROSS ANOTHER RWY. I DIDN'T SEE ANY DOUBLE YELLOW MARKINGS ON MY WAY BACK. I DO FEEL THE TWR SHOULD HAVE TOLD ME UPON MY LNDG TO 'MAKE A R ON ALPHA; CONTACT GND.' I THEN WOULD HAVE STOPPED UPON CLRING 6/24. I WAS NOT AWARE ANOTHER RWY WAS IN USE FOR LNDG TFC. I ALSO SHOULD NOT HAVE ASSUMED I WAS CLRED TO TAXI TO THE FBO BUT I DID. THERE REALLY WAS NO CLOSE CALL AS THE INCOMING PLT SAW ME AND DID A GAR ON HIS OWN BUT I FELT BADLY IN XING AN ACTIVE RWY WITHOUT A CLRNC.