If A is a subset of the set of reflections of a finite Coxeter group W, we define a sub-mathbb Z-module cal DA(W) of the group algebra {mathbb Z} W. We discuss cases where this submodule is a subalgebra. This family of subalgebras includes strictly the Solomon descent algebra, the group algebra and, if W is of type B, the Mantaci¿Reutenauer algebra
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