  Let $\Sigma$ be the Davis complex for a Coxeter system (W,S). The
automorphism group G of $\Sigma$ is naturally a locally compact group, and a
simple combinatorial condition due to Haglund--Paulin determines when G is
nondiscrete. The Coxeter group W may be regarded as a uniform lattice in G. We
show that many such G also admit a nonuniform lattice $\Gamma$, and an infinite
family of uniform lattices with covolumes converging to that of $\Gamma$. It
follows that the set of covolumes of lattices in G is nondiscrete. We also show
that the nonuniform lattice $\Gamma$ is not finitely generated. Examples of
$\Sigma$ to which our results apply include buildings and non-buildings, and
many complexes of dimension greater than 2. To prove these results, we
introduce a new tool, that of "group actions on complexes of groups", and use
this to construct our lattices as fundamental groups of complexes of groups
with universal cover $\Sigma$.
