Orbifold conformal blocks and the stack of pointed G-covers

Starting with a vertex algebra V, a finite group G of automorphisms of V, and a suitable collection of twisted V-modules, we construct (twisted) D-modules on the stack of pointed G-covers, introduced by Jarvis, Kaufmann, and Kimura. The fibers of these sheaves are spaces of orbifold conformal blocks defined in joint work with Edward Frenkel. The key ingredient is a G-equivariant version of the Virasoro uniformization theorem.