  We study Kazhdan-Lusztig cells and the corresponding representations of
right-angled Coxeter groups and Hecke algebras associated to them. In case of
the infinite groups generated by reflections in the hyperbolic plane about the
sides of right-angled polygons we obtain an explicit description of the left
and two-sided cells. In particular, we prove that there are infinitely many
left cells but they all form only three two-sided cells.
