  In this paper, we give a Verlinde formula for computing the ranks of the
bundles of twisted conformal blocks associated with a simple Lie algebra
equipped with an action of a finite group $\Gamma$ and a positive integral
level $\ell$ under the assumption that "$\Gamma$ preserves a Borel". As a
motivation for this Verlinde formula, we prove a categorical Verlinde formula
which computes the fusion coefficients for any $\Gamma$-crossed modular fusion
category as defined by Turaev. To relate these two versions of the Verlinde
formula, we formulate the notion of a $\Gamma$-crossed modular functor and show
that it is very closely related to the notion of a $\Gamma$-crossed modular
fusion category. We compute the Atiyah algebra and prove (with same
assumptions) that the bundles of $\Gamma$-twisted conformal blocks associated
with a twisted affine Lie algebra define a $\Gamma$-crossed modular functor.
Along the way, we prove equivalence between a $\Gamma$-crossed modular functor
and its topological analogue. We then apply these results to derive the
Verlinde formula for twisted conformal blocks. We also explicitly describe the
crossed S-matrices that appear in the Verlinde formula for twisted conformal
blocks.
