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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. [ABSTRACT FROM AUTHOR]

The article presents a mathematical study on the finite generation of Tate cohomology (TC) of a finite group with coefficients in a indecomposable nonprojective module. It is proved that if the finite group has periodic cohomology then all finitely generated modules over the finite group finitely generate TC. Also mentioned is a conjecture on the equivalence of support variety of the module and the maximal ideals. Several theorems and their proofs related to the study are also presented.