  Let $T_1$ and $T_2$ be homogeneous trees of even degree $\ge 4$. A BM group
$\Gamma$ is a torsion free discrete subgroup of $\aut (T_1) \times \aut (T_2)$
which acts freely and transitively on the vertex set of $T_1 \times T_2$. This
article studies dynamical systems associated with BM groups. A higher rank
Cuntz-Krieger algebra $\mathcal A(\G)$ is associated both with a 2-dimensional
tiling system and with a boundary action of a BM group $\Gamma$. An explicit
expression is given for the K-theory of $\mathcal A(\G)$. In particular
$K_0=K_1$. A complete enumeration of possible BM groups $\G$ is given for a
product homogeneous trees of degree 4, and the K-groups are computed.
