0.1. Overview. Let G be a connected reductive group over a finite field F_q and let G(K-circumflex) be the corresponding group over the local field K-circumflex = F_q((t)). Let G(O-circumflex) is contained in G(K-circumflex) be a maximal compact subgroup of G(K-circumflex) (here (Q-circumflex) = F_q[t]) and let H_(sph) denote the Hecke algebra of G(K-circumflex)) with respect to G(O-circumflex).
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