2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71389We introduce analogues of the Hopf algebra of Free quasi-symmetric functions with bases labelled by colored permutations. As applications, we recover in a simple way the descent algebras associated with wreath products $Γ\wr\SG_n$ and the corresponding generalizations of quasi-symmetric functions. Also, we obtain Hopf algebras of colored parking functions, colored non-crossing partitions and parking functions of type $B$.11 pages, AMS LaTexCombinatoricstext