[Tregard]

The official Crash Bandicoot website, owned and operated by Activision, has been taken down. The latest archived version of the site is from this past summer, when rumors of a Sony acquisition of the franchise started popping up.
Additionally, the Crash Bandicoot brand has been completely removed from Activision's main website, and any search through their homepage no longer yields any results. Previously, links to their licensed Crash games were available. Also, their support pages no longer offer support for Crash: Mind Over Mutant (the last game released), or their iOS kart racers.
Kudos to /u/holmesy25 in /r/crashbandicoot for pointing it out. This may be the most concrete evidence so far backing up the possibility of Crash Bandicoot no longer being an Activision owned IP.

This is a still from a recent PS4 advert: