  The free loop space of a Lie group is homeomorphic to the product of the Lie
group itself and its based loop space. We show that the coproduct on the
homology of the free loop space that was introduced by Goresky and Hingston
splits into the diagonal map on the group and a based coproduct on the homology
of the based loop space. This result implies that the coproduct is trivial for
even-dimensional Lie groups. Using results by Bott and Samelson, we show that
the coproduct is trivial as well for a large family of simply connected Lie
groups.
