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Atiyah motivic theorem for the special group SL_d

We exploit calculations of the representations rings of linear group GLd and the special group SLd [4] and the various morphisms between them to deduce morphisms between their associated completed rings. From [15], where Riou proves a motivic Atiyah isomorphism for the linear group GLd wich generalises Atiyah isomorphism, for finite groups [1], between the completed representations ring and the ring of the K-theory of the classifying space, we prove a motivic Atiyah isomorphism for the special group SLd.