Semiinfinite sheaves on affine flag varieties

We study a category of semiinfinite sheaves on the affine flag variety of a connected reductive algebraic group, with coefficients in a field (of arbitrary characteristic different from that of the base field), generalizing some results of Gaitsgory and showing that this category behaves like familiar categories of sheaves on flag varieties in many respects. Our interest is motivated by expected relations with representation theory of the Lie algebra of the Langlands dual reductive group.