  Let $\G$ be a group of type rotating automorphisms of an affine building
$\cB$ of type $\wt A_2$. If $\G$ acts freely on the vertices of $\cB$ with
finitely many orbits, and if $\Omega$ is the (maximal) boundary of $\cB$, then
$C(\Om)\rtimes \G$ is a p.i.s.u.n. $C^*$-algebra. This algebra has a structure
theory analogous to that of a simple Cuntz-Krieger algebra and is the
motivation for a theory of higher rank Cuntz-Krieger algebras, which has been
developed by T. Steger and G. Robertson. The K-theory of these algebras can be
computed explicitly in the rank two case. For the rank two examples of the form
$C(\Om)\rtimes \G$ which arise from boundary actions on $\wt A_2$ buildings,
the two K-groups coincide.
