  The quasisymmetric generating function of the set of permutations whose
inverses have a fixed descent set is known to be symmetric and Schur-positive.
The corresponding representation of the symmetric group is called the descent
representation. In this paper, we provide an extension of this result to
colored permutation groups, where Gessel's fundamental quasisymmetric functions
are replaced by Poirier's colored quasisymmetric functions. For this purpose,
we introduce a colored analogue of zigzag shapes and prove that the
representations associated with these shapes coincide with colored descent
representations studied by Adin, Brenti and Roichman in the case of two colors
and Bagno and Biagioli in the general case. Additionally, we provide a colored
analogue of MaMahon's alternating formula which expresses ribbon Schur
functions in the basis of complete homogeneous symmetric functions.
