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