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