  We give an a priori construction of the two-dimensional reduction of
three-dimensional quantum Chern-Simons theory. This reduction is a
two-dimensional topological quantum field theory and so determines to a
Frobenius ring, which here is the twisted equivariant K-theory of a compact Lie
group. We construct the theory via correspondence diagrams of moduli spaces,
which we "linearize" using complex K-theory. A key point in the construction is
to consistently orient these moduli spaces to define pushforwards; the
consistent orientation induces twistings of complex K-theory. The
Madsen-Tillmann spectra play a crucial role.
