  If $A$ is a subset of the set of reflections of a finite Coxeter group $W$,
we define a sub-${\mathbb{Z}}$-module ${\mathcal{D}}_A(W)$ of the group algebra
${\mathbb{Z}} W$. We provide examples where this submodule is a subalgebra.
This family of subalgebras includes strictly the Solomon descent algebra and,
if $W$ if of type $B$, the Mantaci-Reutenauer algebra.
