B767 FLC ASSUMES DIRECTION OF TURN ONTO TXWY EXITING RWY AND IS CHALLENGED BY ORD GND CTL AS TURNING IN THE WRONG DIRECTION.

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LNDG BY FO ON RWY 27R; WHILE STILL ON LNDG ROLLOUT (120-100 KTS); TWR ISSUES INSTRUCTIONS TO EXIT TXWY 'C'... WE WERE IN PROCESS OF GETTING READY TO XFER ACFT CTL TO ME (CAPT) AND DID NOT CLRLY UNDERSTAND TWR INSTRUCTIONS; EXCEPT 'TURN L ON CHARLIE.' I IMMEDIATELY TOOK ACFT CTL AND APPLIED MORE BRAKING SINCE 'C' EXIT WAS COMING UP FAST. TAKING 'C' EXIT (45-60 KTS); TWR AGAIN SAID CONTINUE...ALL VERY FAST. I KNEW I HAD TO TAXI ENOUGH TO CLR TAIL OF RWY; WHICH I DID; THEN BEGAN L TURN WHEN TOLD TO CHANGE TO A GND FREQ WHO BEGAN TO TELL US THAT WE WERE NOT TO TURN BUT GO ON TXWY B; THAT WE WERE TOLD TWICE BY TWR; SO ACFT LNDG BEHIND US COULD ALSO CLR ON 'C.' 1) WE WERE STILL 'FLYING THE ACFT' WHEN INSTRUCTIONS WERE ISSUED AT 100 KTS. 2) CREW SWAPPING JOBS EARLY BECAUSE TWR WANTED US TO TURN EARLY ON 7900 FT RWY. 3) #1 PRIORITY TO CLR TAIL IN RWY. #2 PRIORITY TO SLOW ACFT FOR 90 DEG TURNS; 10 KTS. 4) WE'RE ON VISUAL APCH; SO ACFT BEHIND US SHOULD HAVE SLOWED DOWN INCREASING SPACING. 5) NO HOLD SHORT OF RWY IN USE. IF WE HAD USED 500 FT MORE; TWR MIGHT HAVE SENT ACFT GO AROUND SPACING MUCH TOO TIGHT! 6) ACFT BEHIND US WAS A DC9 TURNED DOWN 'TXWY C' BEHIND US; NO REAL CLOSE ENCOUNTER. WAS EASIER TO STOP THAN OUR 400000 LB ACFT! NO TAXI INSTRUCTIONS UNTIL ACFT CLR OF RWY. SUPPLEMENTAL INFO FROM ACN 525534: NEITHER I OR THE CAPT PROCESSED OR ACKNOWLEDGED THESE INSTRUCTIONS; AS WE WERE AT THAT TIME DISCUSSING WHETHER WE WOULD PLAN AN EXIT AT THE HIGH SPD OR ADVISE TWR WE WOULD BE USING FULL LENGTH. THE TWR CTLR WAS VERY CONCERNED WITH CLOSELY SPACED LNDG TFC BEHIND US. THE CTLR AGAIN ISSUED TURN-OFF INSTRUCTIONS AT APPROX 60 KTS STATING 'TURN L AT TXWY C; KEEP ROLLING AND GO TO GND.' AT THIS POINT WE WERE STILL DOING SOP FLOWS FOR TERMINATING REVERSE THRUST WITH AIRSPD CALLOUTS; AND XFERRING ACFT CTL. I THEN READ BACK THESE INSTRUCTIONS; WE CLRED AT TXWY C IMMEDIATELY AND WENT TO GND. THE CAPT CHOSE TO TURN L TOWARD OUR RAMP; VICE R ONTO TXWY B. THEY THEN STATED THAT NOT CONTINUING AFTER CLRING THE RWY 'COULD CREATE A DANGEROUS SIT.' ACFT SHOULD BE ABLE TO EXPECT TO COMPLETE THE LNDG PHASE BEFORE GETTING URGENT AND LENGTHY TAXI INSTRUCTIONS. SENDING AN ACFT AROUND SHOULD BE A SECONDARY CONCERN.