  Given a complete CAT(0) space $X$ endowed with a geometric action of a group
$\Gamma$, it is known that if $\Gamma$ contains a free abelian group of rank
$n$, then $X$ contains a geometric flat of dimension $n$. We prove a converse
of this statement in the special case where $X$ is a convex subcomplex of the
CAT(0) realization of a Coxeter group $W$, and $\Gamma$ is a subgroup of $W$.
In particular a convex cocompact subgroup of a Coxeter group is
Gromov-hyperbolic if and only if it does not contain a free abelian group of
rank 2. Our result also provides an explicit control on geometric flats in the
CAT(0) realization of arbitrary Tits buildings.
