Authenticating and evaluating my Omega watch

Got this Omega, hoping for help identifying it and getting a sense of value.
Case back is stamped "W.W.W.", broad arrow, "Y22668", and "10582903" (photos attached). Dial has the Omega logo with a circled T underneath, arabic numerals, broad arrow at 6, and what looks like a center-seconds hand rather than a sub-dial. There's a handwritten "R2.3.71" scratched inside the case back.
Movement is only marked "OMEGA" and "SWISS" - no visible caliber number that I can find.
It's currently running. Attaching photos of the dial, case back, inner case back, and movement.
Would appreciate any thoughts on whether this is an original WWW case with a later service-replaced dial, and roughly what it might be worth in this condition.

Looks like a fake to me. Among other things It has 167.005 etched on the case back inside, this is an Omega Constellation chronometer reference, which would have a 551 movement and that movement is definitely not a 551.