Had a problem while doing a RNAV approach into St. Kitts. The approach to RW07 was going fine, I was in VNAV/LNAV and descending on speed and on profile. A few miles past OMONO, the aircraft began to bank into the 90 degree turn to get aligned with the runway, as was to be expected. That’s when the problem occurred. Instead of rolling out on a course of 071, inbound to DUSUL, the jet continued turning left. It was almost as if it was trying to go back and physically overfly LOMDO. See the chart below. It went nearly 270 degrees around before I disconnected the AP and handflew a (sloppy) approach and landing. Any idea what I did wrong?
