  Mathai, Melrose, and Singer introduced the notion of projective elliptic
operators on manifolds equipped with an Azumaya bundle. In this note we compute
the equivariant index of transversally elliptic operators that are the pullback
of projective elliptic operators on the trivialization of the Azumaya bundle.
It encompasses the fractional index formula of projective elliptic operator by
Mathai-Melrose-Singer.
