  Let $\Gamma$ be a finite group acting on a simple Lie algebra $\mathfrak{g}$
and acting on a $s$-pointed projective curve $(\Sigma, \vec{p}=\{p_1, \dots,
p_s\})$ faithfully (for $s\geq 1$). Also, let an integrable highest weight
module $\mathscr{H}_c(\lambda_i)$ of an appropriate twisted affine Lie algebra
determined by the ramification at $p_i$ with a fixed central charge $c$ is
attached to each $p_i$. We prove that the space of twisted conformal blocks
attached to this data is isomorphic to the space associated to a quotient group
of $\Gamma$ acting on $\mathfrak{g}$ by diagram automorphisms and acting on a
quotient of $\Sigma$. Under some mild conditions on ramification types, we
prove that calculating the dimension of twisted conformal blocks can be reduced
to the situation when $\Gamma$ acts on $\mathfrak{g}$ by diagram automorphisms
and covers of $\mathbb{P}^1$ with 3 marked points. Assuming a twisted analogue
of Teleman's vanishing theorem of Lie algebra homology, we derive an analogue
of the Kac-Walton formula and the Verlinde formula for general $\Gamma$-curves
(with mild restrictions on ramification types). In particular, if the Lie
algebra $\mathfrak{g}$ is not of type $D_4$, there are no restrictions on
ramification types.
