The isometry groups of Riemannian orbifolds

We prove that the isometry group ?(\(\mathcal{N}\)) of an arbitrary Riemannian orbifold \(\mathcal{N}\), endowed with the compact-open topology, is a Lie group acting smoothly and properly on \(\mathcal{N}\). Moreover, ?(\(\mathcal{N}\)) 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.