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