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Monodromic systems on affine flag manifolds

There has been recently substantial progress in the programme of expressing the characters of irreducible modular representations of a semisimple group over a field of positive characteristic in terms of combinatorics of affine Hecke algebras (see Andersen et al. 1992; Kazhdan & Lusztig 1979). This paper is a further contribution to this programme: I explain why in the non-simply laced case, the ‘dual’ affine Weyl group is needed and why in this case it is necessary to use monodromic systems (certain local systems defined on subvarieties of a line bundle) over an affine flag manifold.