Noncommutative poisson structures on orbifolds

In this paper, we compute the Gerstenhaber bracket on the Hoch- schild cohomology of C∞(M) × 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∞(M) × G when M is a symplectic manifold. We also discuss examples of deformation quantizations of these noncommutative Poisson structures.