Base change and K-theory for orbits of p-adic GL(n)

Abstract

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 $C_r^*(G//I)$. 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.