Abstract: Affine Schubert varieties are certain subvarieties of the affine Grassmannian which show up in geometric contexts related to the Langlands program. Faltings and Pappas-Rapoport showed that in equal characteristic p, affine Schubert varieties are normal, Cohen-Macaulay, and Frobenius split. In previous work for split groups, I added global F-regularity to this list, with consequences for the theory of perverse mod p sheaves in characteristic p. In this talk, I will explain joint work with J. Lourenço where we explore similar questions for groups of mixed characteristic.