Hopf algebra characters and multiple zeta values

Multiple zeta values can be thought of as images of a
homomorphism Z from the algebra QSym of quasi-symmetric
functions (an extension of the algebra of symmetric functions)
to the reals.  If this homomorphism is suitably defined, one
has the pleasing formula Z(H(t)) = Gamma(1-t), where H(t)
is the generating function of the complete symmetric
functions.  Aguilar, Bergeron and Sotille introduced the
idea of splitting a character on a Hopf algebra (which is
what Z: QSym -> R is) into odd and even factors.  We will
show how this splitting applies to our character Z, and how
the splitting facilitates computations of Z restricted to the
symmetric functions.