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There is a well-known combinatorial definition, based on ordered setpartitions, of the semigroup of faces of the braid arrangement. We generalizethis definition to obtain a semigroup Sigma_n^G associated with G wr S_n, thewreath product of the symmetric group S_n with an arbitrary group G. Techniquesof Bidigare and Brown are adapted to construct an anti-homomorphism from theS_n-invariant subalgebra of the semigroup algebra of Sigma_n^G into the groupalgebra of G wr S_n. The generalized descent algebras of Mantaci and Reutenauerare obtained as homomorphic images when G is abelian.

A semigroup approach to wreath-product extensions of Solomon's descent algebras