PCP characterization of NP
The PCP Theorem is a theorem about checking proofs, i.e. that there exist locally checkable proof systems, ones that don't "turn from non-accepting to accepting by changes that would be insignificant by any reasonable metric" (quote, top of page 2 here).

Simply stated, it's not directly related to "efficient computation" at all -- more of "efficient checking," for an appropriate definition of efficient.

I suppose it might be possible to use the machinery and terminology of PCPs to attack P vs NP, but it seems likely that such an argument would have a simpler statement under a different model and mode of thought to me. If nothing else -- I haven't seen any attempts in that direction.