Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups

We construct a subalgebra Sigma'(W-n) of dimension 2(.)3(n-1) of the group algebra of the Weyl group W-n of type B-n containing its usual Solomon algebra and the one of G(n):Sigma'(W-n) is nothing but the Mantaci-Reutenauer algebra but our point of view leads us to a construction of a surjective morphism of algebras Sigma'(W-n)-> ZIrr(W-n). Jollenbeck's construction of irreducible characters of the symmetric group by using the coplactic equivalence classes can then be transposed to W. In an appendix, P. Baumann and C. Hohlweg present in an explicit and combinatorial way the relation between this construction of the irreducible characters of W-n and that of W. Specht.