Maybe it's a Royal Oyster.........
I wonder if these came out around the same time, maybe they got some flak about the Royal Oak one and decided to make it less obvious. If they did get some legal warnings, maybe this was just the last of the cases and bracelets being used....
It very much resembles a Rolex OysterQuartz, there were two main models, one with fluted bezel and one with smooth. The fluted bezel one had a VERY Royal Oak type bracelet, and the smooth bezel had a bracelet like we see here. (ref 17000?) If you google it, you can even see the Rolex next to the AP, and it's a wonder there weren't lawsuits of some kind.
I suspect this might be a variant of whatever it was they actually called the Oak one.
Can you make out what the ink stamp says?