Atiyah motivic theorem for the special group SL_d

Abstract

We exploit calculations of the representations rings of linear group GL_d and the special group SL_d [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 GL_d 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 SL_d.