AN ARTCC CTLR CLRED A LR25 ACFT TO AN OCCUPIED ALT THEN TURNED THE ACFT FOR SEPARATION WITH A B737 AT THE SAME ALT. THE LR25 WAS SLOW TO TURN AND LTSS OCCURRED.

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WHILE ON DUTY AS AREA SUPVR IN CHARGE; A CTLR ISSUED A DIRECT CLRNC TO CVG FROM N OF ROD TO AN ACFT. THIS SHOULD HAVE RESULTED IN A R TURN OF 5-10 DEGS FOR THE ACFT. INSTEAD; THE ACFT TURNED L 16 DEGS AND CONFLICTED WITH AN E-NEBOUND ACR. THE ACR HAD AN RA TO CLB; BUT ALREADY AT FL370 COULD NOT; SO THE ACR TOOK EVASIVE ACTION TO THE R. TCASII WAS NOT A CAUSE OF THIS ERROR. SUPPLEMENTAL INFO FROM ACN 357756: 1 MIN AFTER LEVELOFF AT FL370; CLRED TO ROD VOR; ZOB CLRED ACFT #1 DIRECT TO CVG VOR. ACFT #1 BEGAN TURNING WITH AUTOPLT ENGAGED. AT APPROX 1 MIN LATER ARTCC CTLR ADVISED ACFT #1 TO TURN TO HDG 270 DEGS IMMEDIATELY AND ACFT #2 TO TURN TO HDG 090 DEGS IMMEDIATELY. ACFT #2 ANNOUNCED THEY HAD A TCASII WARNING. ARTCC CTLR ANNOUNCED A LEARJET WAS E OF COURSE; IN RESPONSE TO ACFT #2 INQUIRY. ORIGINAL TRACK OF ACFT #1 WAS 193 DEGS AND NEW TRACK TO CVG WAS 215 DEGS AND ACFT #1 WAS IN A CONTINUOUS R TURN AT TIME OF EVENT. SUPPLEMENTAL INFO FROM ACN 357750: PNF NOTICED TURN RATE SLOWER THAN NORMAL ON HEADING BUG TURN MODE OF AUTOPLT AND BEGAN TO INVESTIGATE FOR AUTOPLT MALFUNCTION. ARTCC CTLR ADVISED ACFT #1 TO TURN TO HDG 270 DEGS IMMEDIATELY AND ACFT #2 TO TURN TO HDG 090 DEGS IMMEDIATELY. ACFT #2 ANNOUNCED THEY HAD TCASII WARNING REQUIRING EVASIVE ACTION. ARTCC CTLR BLAMED INCIDENT (ON CTR FREQ) ON ACFT #1; SAYING THE LEARJET WAS E OF ASSIGNED TRACK. EXCESSIVE DEV FROM CLRED COURSE (PROTECTED AIRSPACE) SEEMS UNLIKELY. INCIDENT IS PROBABLE CTLR ERROR. ACFT #1 WAS PROBABLY CLRED BY ATC TO CLB IN ERROR INTO ACFT #2 PROTECTED AIRSPACE.