UNAUTHORIZED RWY ENTRY.

Narrative

TAXIING OUT FOR TKOF RWY 10 AT AGC. 2 LIGHT ACFT AHEAD OF US. AS WE APCHED THE INTXN OF THE E/W TAXIWAY AND RWY 5/23; THE CTLR CALLED AND SAID 'MAKE YOUR NEXT R TURN AND YOU ARE #1 FOR TKOF.' STILL FINISHING THE CHKLIST; I GLANCED AT THE RADIO CTL AND SAW BOTH 121.7 (GND) AND 121.1 (TWR) DISPLAYED. A CALL CAME IN; 'AFTER TKOF; MAKE A L TURN TO A HDG OF 360 DEGS; AND CONTACT DEP ON 124.75.' I THOUGHT THE SAME CTLR WAS WORKING BOTH 121.7 AND 121.1 AS THE VOICES SOUNDED VERY SIMILAR EARLIER AS WE TAXIED IN. I ASKED THE COPLT TO REQUEST PERMISSION TO BACK TAXI ON THE RWY SO WE COULD USE THE FULL LENGTH; LOOKED BOTH WAYS TO CLR FOR TFC AND SLOWLY CONTINUED TO TAXI. ONLY THEN DID THE GND CTLR STATE 'HOLD YOUR POS AND CONTACT THE TWR.' WE NOW HAD OUR NOSE ON RWY 10. I CONTACTED TWR AND WAS CLRED TO BACK TAXI AND TKOF. THE CREW MADE AN ERRONEOUS ASSUMPTION-COMPOUNDED BY THE FACT THAT THEY WEREN'T EXPECTING THE SHORT CUT TO THE RWY AND WERE STILL FINISHING UP THE CHKLISTS WHEN THE AFTER TKOF INFO WAS RECEIVED. GND CTL COULD HAVE BEEN MORE SPECIFIC AND SAID 'HOLD SHORT OF THE RWY AND CONTACT TWR.'