  An important result of Arkhipov-Bezrukavnikov-Ginzburg relates constructible
sheaves on the affine Grassmannian to coherent sheaves on the dual Springer
resolution. In this paper, we prove a positive-characteristic analogue of this
statement, using the framework of "mixed modular sheaves" recently developed by
the first author and Riche. As an application, we deduce a relationship between
parity sheaves on the affine Grassmannian and Bezrukavnikov's "exotic
t-structure" on the Springer resolution.
