  Let $\mathcal{G}$ be a parahoric Bruhat-Tits group schemes arising from a
$\Gamma$-curve $C$ and a certain $\Gamma$-action on a simple algebraic group
$G$ for some finite cyclic group $\Gamma$. We prove the flatness of
Beilinson-Drinfeld Schubert varieties of $\mathcal{G}$, we determine the
rigidified Picard group of the Beilinson-Drinfeld Grassmannian ${\rm
Gr}_{\mathcal{G},C^n}$ of $\mathcal{G}$, and we establish the factorizable and
equivariant structures on rigidified line bundles on ${\rm
Gr}_{\mathcal{G},C^n}$.
  We develop an algebraic theory of global Demazure modules of twisted current
algebras, and using our geometric results we prove that when $C =
\mathbb{A}^1$, the spaces of global sections of line bundles on BD Schubert
varieties of $\mathcal{G}$ are dual to the twisted global Demazure modules.
This generalizes the work of Dumanski-Feigin-Finkelberg in the untwisted
setting,

Representation Theory;Algebraic Geometry