Let ℚ p be the field of p-adic numbers and 𝔾 a split connected reductive group scheme over ℤ p . In this work we will introduce a sheaf of twisted arithmetic differential operators on the formal flag variety of 𝔾, associated to a general character. In particular, we will generalize the results of [21], concerning the 𝒟 † -affinity of the smooth formal flag variety of 𝔾, of certain sheaves of p-adically complete twisted arithmetic differential operators associated to an algebraic character, and the results of [24] concerning the calculation of the global sections.