  Let F be a nonarchimedean local field and let G = GL(n) = GL(n,F). Let E/F be
a finite Galois extension. We investigate base change E/F at two levels: at the
level of algebraic varieties, and at the level of K-theory. We put special
emphasis on the representations with Iwahori fixed vectors, and the tempered
spectrum of GL(1) and GL(2). In this context, the prominent arithmetic
invariant is the residue degree f(E/F).
