Let E=F be a finite Galois extension of a nonarchimedean local field F with zero characteristic and let G = GL(n) = GL(n, F). We investigate base change E/F at the level of K-theory for the spherical C*-algebra C_r^*(G//K) and the Iwahori C*-algebra C_r^*r (G//I). Then we proceed to more abstract compact orbits of Langlands parameters and show that, at the level of the K-theory group K1, base change is multiplication by the residue degree f = f(E/F), generalizing previous results.

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Local field,General linear group,C*-algebra,Base change,K-theory