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We prove that the isometry group I(N ) of an arbitrary Riemannian orbifold N , endowed with the compact-open topology, is a Lie group acting smoothly and properly on N . Moreover, I(N ) admits a unique smooth structure that makes it into a Lie group. We show in particular that the isometry group of each compact Riemannian orbifold with a negative definite Ricci tensor is finite, thus generalizing the well-known Bochner's theorem for Riemannian manifolds.

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