  The purpose of the present article is to define and study a new class of
descent algebras, called twisted descent algebras. These algebras are
associated to the Barratt-Joyal theory of twisted bialgebras in the same way
than classical descent algebras are associated to classical bialgebras. The
formal properties of twisted descent algebras seem particularly meaningful in
view of applications to discrete probabilities, to the geometry of Coxeter
groups and buildings, and to symmetric group combinatorics.
