  We show some of the conjectures of Pappas and Rapoport concerning the moduli
stack of $\mathcal{G}$-torsors on a curve C, where $\mathcal{G}$ is a
semisimple Bruhat-Tits group scheme on C. In particular we prove the analog of
the uniformization theorem of Drinfeld-Simpson in this setting. Furthermore we
apply this to compute the connected components of these moduli stacks and to
calculate the Picard group of the stack of torsors in case $\mathcal{G}$ is
simply connected.
