CL65 CREW CREATES TFC CONFLICT WITH DSNDING ACFT AFTER TURNING THE WRONG WAY ON A VECTOR IN ZID AIRSPACE.

Narrative

THE FOCUS OF THE EVENT IS A POSSIBLE TFC CONFLICT BTWN MY ACFT AND ANOTHER. MY ACFT WAS CLBING ON COURSE TO AN ASSIGNED ALT OF FL290. ATC ISSUED A VECTOR: R TURN 15 DEGS. APPARENTLY; WHEN THIS SEEMED INSUFFICIENT; THEY ISSUED AN ADDITIONAL R 15 DEGS. DUE APPARENTLY TO A MISUNDERSTANDING OF THE CLRNC FROM ATC; THE PF TURNED L INSTEAD OF R. AT APPROX FL255; ATC ASSIGNED A NEW ALT OF FL260. WE HAD SUFFICIENT TIME TO RESET THE ALT ALERTER AND FOR THE AUTOPLT TO LEVEL THE ACFT AT FL260 WITHOUT EXCEEDING THE ALT. THE CONFLICTING TFC WAS RECLRED TO STOP DSCNT AT FL270. ATC ASKED AND RECEIVED VERIFICATION THAT THE CONFLICT ACFT HAD LEVELED AT FL270. I HAD ACQUIRED THE CONFLICT ACFT BOTH ON THE TCASII AND VISUALLY. EVEN THOUGH TCASII PRODUCED AN RA; WITH CONFLICT ACFT IN SIGHT; WE HAD SUFFICIENT VERT SEPARATION; HORIZ DISTANCE AND DIVERGENT COURSES THAT NO DIVERSION ACTION WAS DEEMED NECESSARY. I BELIEVE CONTRIBUTING FACTORS TO THE SIT WERE AS FOLLOWS: 1) SCHEDULED REDUCED REST PERIOD PREVIOUS NIGHT (WITH POOR SLEEP DUE TO LCL FACTORS). 2) FAILURE OF ATC CTLR TO ISSUE A SPECIFIC HDG FOR VECTOR; AS OPPOSED TO VAGUE TURNS. 3) INSUFFICIENT SUPERVISION OF PF BY PNF DUE TO DISTR (COMMERCIAL CHART UPDATES).