  Let $G$ be a simple algebraic group over an algebraically closed field $k$.
Let $\Gamma$ be a finite group acting on $G$. We classify and compute the local
types of $(\Gamma, G)$-bundles on a smooth projective $\Gamma$-curve in terms
of the first non-abelian group cohomology of the stabilizer groups at the
tamely ramified points with coefficients in $G$. When $\text{char}(k)=0$, we
prove that any generically simply-connected parahoric Bruhat--Tits group scheme
can arise from a $(\Gamma,G_{\text{ad}})$-bundle. We also prove a local version
of this theorem, i.e. parahoric group schemes over the formal disc arise from
constant group schemes via tamely ramified coverings.
