  We construct an S^1-equivariant prospectrum that models the Atiyah dual of a
free loop space of a manifold. By applying a suitably completed S^1-equivariant
K-theory to the Atiyah dual, we show how to recover the Witten genus of the
manifold. The main technical tool is a Tits building for the loop group. We use
this building to construct a dualizing spectrum for the loop group and relate
it to work of Freed, Hopkins and Teleman.
