We prove the theorem in the title by constructing an action of a Coxeter group on a product of trees.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm174-1-4,
author = {Tadeusz Januszkiewicz},
title = {For Coxeter groups $z^{|g|}$ is a coefficient of a uniformly bounded representation},
journal = {Fundamenta Mathematicae},
volume = {173},
year = {2002},
pages = {79-86},
zbl = {1038.20025},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm174-1-4}
}
Tadeusz Januszkiewicz. For Coxeter groups $z^{|g|}$ is a coefficient of a uniformly bounded representation. Fundamenta Mathematicae, Tome 173 (2002) pp. 79-86. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm174-1-4/