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In the apartment corresponding to a chosen maximal split torus of T, we fix a hyperspecial vertex and denote by K the corresponding maximal compact subgroup of G. Given an irreducible smooth k-representation $\\rho$ of K, we construct an isomorphism from the affine semigroup k-algebra of the dominant cocharacters of T onto the Hecke algebra $H(G, \\rho)$. 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