  The geometric Satake isomorphism is an equivalence between the categories of
spherical perverse sheaves on affine Grassmanian and the category of
representations of the Langlands dual group. We provide a similar description
for derived categories of l-adic sheaves on an affine flag variety which are
geometric counterparts of a maximal commutative subalgebra in the Iwahori Hecke
algebra; of the anti-spherical module over this algebra; and of the space of
Iwahori-invariant Whitakker functions.
