CVG CTLR CHRONICLES PLT NAV ERROR THAT RESULTED IN NEAR LOSS OF SEPARATION AT 9000 FT BTWN ARR AND DEP ACFT.

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I WAS WORKING ARR W AT CVG. ACR X CRJ2 WAS INBOUND TO CVG; FILED RID 217 MEEKR DIRECT CVG. IN AN ATTEMPT TO SHORTCUT ACR X; I ISSUED A 190 DEG HDG TO JOIN THE CVG 320 DEG RADIAL. ACR X TURNED ONTO THE CVG 340 DEG RADIAL. I WAS WORKING 5 OTHER ACFT AT THE TIME; AND IN THE MIDDLE OF MY SCAN SAW THE ACFT HEAD-ON WITH ANOTHER SIMILAR CALL SIGN DEPARTING CVG DIRECT MIE CLBING THROUGH 8700 FT FOR 13000 FT; I ASKED THE PLT IF HE WAS SHOWING HIMSELF ON THE 320 DEG RADIAL; AND HE INDICATED HE DID. I THEN TURNED HIM TO A 220 DEG HDG USING AN 'IMMEDIATE' CLRNC. THE DEP N CTLR TURNED HIS ACFT ALSO. THE ACFT'S CLOSEST PROX WAS ZERO FT VERT; AND 3.5 MI LATERAL. FOLLOWING THE MIX; I TURNED ACR X BACK TO CVG VOR; AND ASKED HIM TO ADVISE HIS HDG ONCE HE WAS DIRECT. HE LATER ADVISED THAT '143 DEGS IS DIRECT.' I SHOWED HIM ON THE 323 DEG RADIAL OFF CVG. AN EXACT MATCH; AND STILL N OF WHERE THE ACFT WAS SUPPOSED TO BE INITIALLY. HAD THE DEP CTLR OR MYSELF NOT CAUGHT THE PLT'S ERROR; THE ACFT WOULD HAVE BEEN IN VERY CLOSE PROX. IF THE PLT HAD ANY QUESTION ABOUT HIS CLRNC; HE SHOULD HAVE ASKED; AND THE FACT THE PLANE WAS STILL N OF WHERE HE SHOULD HAVE BEEN MAKES ME WONDER ABOUT WHAT EXACTLY THE CREW WAS DOING.