  Let $X$ be a finite connected graph, each of whose vertices has degree at
least three. The fundamental group $\Gamma$ of $X$ is a free group and acts on
the universal covering tree $\Delta$ and on its boundary $\partial \Delta$,
endowed with a natural topology and Borel measure. The crossed product
$C^*$-algebra $C(\partial \Delta) \rtimes \Gamma$ depends only on the rank of
$\Gamma$ and is a Cuntz-Krieger algebra whose structure is explicitly
determined. The crossed product von Neumann algebra does not possess this
rigidity. If $X$ is homogeneous of degree $q+1$ then the von Neumann algebra
$L^\infty(\partial \Delta)\rtimes \Gamma$ is the hyperfinite factor of type
$III_\lambda$ where $\lambda=1/{q^2}$ if $X$ is bipartite, and $\lambda=1/{q}$
otherwise.
