We study multiplicative Dirac structures on Lie groups. We show that the
characteristic foliation of a multiplicative Dirac structure is given by the
cosets of a normal Lie subgroup and, whenever this subgroup is closed, the leaf
space inherits the structure of a Poisson-Lie group. We also describe
multiplicative Dirac structures on Lie groups infinitesimally.Comment: Published in Comptes Rendus Mathematiqu