  We introduce analogs of the Hopf algebra of Free quasi-symmetric functions
with bases labelled by colored permutations. When the color set is a semigroup,
an internal product can be introduced. This leads to the construction of
generalized descent algebras associated with wreath products $\Gamma\wr\SG_n$
and to the corresponding generalizations of quasi-symmetric functions. The
associated Hopf algebras appear as natural analogs of McMahon's multisymmetric
functions. As a consequence, we obtain an internal product on ordinary
multi-symmetric functions. We extend these constructions to Hopf algebras of
colored parking functions, colored non-crossing partitions and parking
functions of type B.
