Already published

with Jacek Swiatkowski,
dvi, ps,
Hyperbolic Coxeter groups of large dimension
Commentarii Math. Helvetici 78(2003) pp.555-583.
We prove a generalization of Vinberg's theorem giving a bound on the dimension Gromov hyperbolic Poincare duality groups.
On the other hand we construct Gromov hyperbolic Coxeter groups of arbitrarily large virtual cohomological dimension.

with Mike Davis and Rick Scott,
ps Fundamental groups of blowups
Advances in Mathematics vol 177, issue 1, 2003, pp. 115-179
This is a follow up on "Nonpositive curvature of blowups". We take a look at equivariant blowups of arrangements of mirrors coming from (not necessarily finite) reflection group W. Universal cover of such a space is acted on cocompactly by certain extension of W, and the action is very much reminiscent of the reflection group action, though it is not of this type. We study those groups and spaces guided by the above analogy: provide a presentations, construct equivariant nonpositively curved thickenings (thus these groups satisfy the properties from CAT(0) package), construct natural linear representations (BUT we cannot prove these are faithful).

with Swiatoslaw Gal
dvi, ps, "Approximation properties of Baumslag-Solitar groups".
Journal of Lie Theory vol.13 (2003), no.2, pp.383-385 link to the journal,
We show that Baumslag-Solitar groups are both aTmenable and topologically amenable. In fact we discuss a slight generalization of Baumslag-Solitar groups, including Bieri-Strebel groups. In the proof we use Bass-Serre theory.

with Jan Dymara
.dvi , .ps , Cohomology of buildings and of their automorphism groups
Inventiones Mathematicae 150(3)2002, pp. 579-627. link to the journal
It's a long paper, but its definitely worth reading.

"For Coxeter groups z^|g| is a coefficient of a uniformly bounded representation",
Fundamenta Mathematicae 174(2002)pp. 79-86.
You have what is in the title and a little more. Gero Fendler was visiting Wroclaw in Nov/Dec 1998 and lecturing about this property for Coxeter groups of "large type". I noticed that my old argument for right angled groups can be adapted to the general situation.