The isometry groups of Riemannian orbifolds

We prove that the isometry group $\mathfrak{I}(\mathcal{N})$ 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, $\mathfrak{I}(\mathcal{N})$ 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.