Delocalised traces on Hecke algebras of right-angled, hyperbolic type

For every Hecke C*-algebra of right-angled, hyperbolic type, we construct a smooth subalgebra to which traces associated with arbitrary conjugacy classes in the associated Coxeter group extend. We calculate the pairing with K-theory of the delocalised traces arising this way, showing that it is faithful on K-theory.