  In this paper, we compute the Gerstenhaber bracket on the Hoch-schild
cohomology of $C^\infty(M)\rtimes G$ for a finite group $G$ acting on a compact
manifold $M$. Using this computation, we obtain geometric descriptions for all
noncommutative Poisson structures on $C^\infty(M)\rtimes G$ when $M$ is a
symplectic manifold. We also discuss examples of deformation quantizations of
these noncommutative Poisson structures.
