  We define an imbedding of the Hecke algebra module carried by the involutions
in a Weyl group W (defined by the author and Vogan) into a completion of the
Hecke algebra. An analogous result is proved for any Coxeter group. A variant
of the construction gives an imbedding of the biregular representation of a
Hecke algebra of W in a completion of the Hecke algebra of W^2.
