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.
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