  Starting from an operad, one can build a family of posets. From this family
of posets, one can define an incidence Hopf algebra. By another construction,
one can also build a group directly from the operad. We then consider its Hopf
algebra of functions. We prove that there exists a surjective morphism from the
latter Hopf algebra to the former one. This is illustrated by the case of an
operad built on rooted trees, the $\NAP$ operad, where the incidence Hopf
algebra is identified with the Connes-Kreimer Hopf algebra of rooted trees.
