Asymptotic K-theory for groups acting on (A)over-tilde(2) buildings

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