Quantum affine algebras at roots of unity and equivariant K-theory

We show that the algebra homomorphism U-q (<(gl)over cap>(n)) --> K-GLd x C* (Z) x C(q) constructed by Ginzburg and Vasserot between the quantum affine algebra of type gl(n) and the equivariant K-theory group of the Steinberg variety (of incomplete flags), specializes to a surjective homomorphism U-epsilon(res) (<(gl)over cap>(n)) --> K-epsilon(GLd x C)* (Z). In particular, this shows that the parameterization of irreducible U-epsilon(res) (<(sl)over cap>(n))-modules and the multiplicity formulaes of [6], [8] are still valid when epsilon is a root of unity. (C) Academie des Sciences/Elsevier, Paris.