  We extend the geometric approach to vertex algebras developed by the first
author to twisted modules, allowing us to treat orbifold models in conformal
field theory. Let $V$ be a vertex algebra, $H$ a finite group of automorphisms
of $V$, and $C$ an algebraic curve such that $H \subset \on{Aut}(C)$. We show
that a suitable collection of twisted $V$--modules gives rise to a section of a
certain sheaf on the quotient $X=C/H$. We introduce the notion of conformal
blocks for twisted modules, and analyze them in the case of the Heisenberg and
affine Kac-Moody vertex algebras. We also give a chiral algebra interpretation
of twisted modules.
