  In this paper we provide a "combinatorial" description of the category of
tilting perverse sheaves on the affine flag variety of a reductive algebraic
group, and its free-monodromic variant, with coefficients in a field of
positive characteristic. This provides a replacement for the familiar "Soergel
theory" for characteristic-0 coefficients, and the second step in our project
towards the construction of an equivalence of categories relating the two
natural geometric realizations of the associated affine Hecke algebra in the
case of positive-characteristic coefficients.
