  In recent years, the usual BPHZ algorithm for renormalization in perturbative
quantum field theory has been interpreted, after dimensional regularization, as
a Birkhoff decomposition of characters on the Hopf algebra of Feynman graphs,
with values in a Rota-Baxter algebra of amplitudes. We associate in this paper
to any such algebra a universal semi-group (different in nature from the
Connes-Marcolli "cosmical Galois group"). Its action on the physical amplitudes
associated to Feynman graphs produces the expected operations: Bogoliubov's
preparation map, extraction of divergences, renormalization. In this process a
key role is played by commutative and noncommutative quasi-shuffle bialgebras
whose universal properties are instrumental in encoding the renormalization
process.
