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Let us suppose that $\mathbb{Q}_p$ is the field of $p$-adic numbers and$\mathbb{G}$ is a split connected reductive group scheme over $\mathbb{Z}_p$.In this work we will introduce a sheaf of twisted arithmetic differentialoperators on the formal flag variety of $\mathbb{G}$, associated to a generalcharacter. We will generalize the arguments of C. Huyghe and T. Schmidt,concerning the $\mathcal{D}^{\dag}$-affinity of the formal flag variety of$\mathbb{G}$, of certain sheaves of $p$-adically complete twisted arithmeticdifferential operators associated to an algebraic character, and thecalculation of the global sections.

A Beilinson-Bernstein theorem for twisted arithmetic differential operators on the formal flag variety