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Let X be projective variety over an algebraically closed field k and G be a finite group with g.c.d.(char(k), |G|) = 1. We prove that any representations of G on a coherent sheaf, ρ : G → End(ℰ), has a natural decomposition ℰ ≃ ⊕ V ⊗k ℱV, where G acts trivially on ℱV and the sum run over all irreducible representations of G over k.