Asymptotic K-theory for groups acting on (A)over-tilde2 buildings

Let Gamma be a torsion free lattice in G = PGL(3, F) where F is a nonarchimedean local field. Then Gamma acts freely on the affine Bruhat-Tits building 3 of G and there is an induced action on the boundary Omega of B. The crossed product C*-algebra A(Gamma) = C(Omega) times sign with bar connected to right of it Gamma depends only on F and is classified by its K-theory. This article shows how to compute the K-theory of A(F) and of the larger class of rank two Cuntz-Krieger algebras.