  Let (G,S) be a finitely generated Coxeter group, such that the Coxeter system
is indecomposable and the canonical bilinear form is indefinite but
non-degenerate. We show that the reduced C-*-algebra of G is simple with unique
normalised trace.
  For an arbitrary finitely generated Coxeter group we prove the validity of a
Haagerup inequality: There exist constants C>0 and a natural number L such that
for a function f in l^2(G) supported on elements of length n with respect to
the generating set S:
  || f * h || <= C(n+1)^{3/2 L} || f || || h ||, forall h in l^2(G).
