  We establish an index theorem for Toeplitz operators on odd dimensional spin
manifolds with boundary. It may be thought of as an odd dimensional analogue of
the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with
boundary. In particular, there occurs naturally an invariant of $\eta$ type
associated to $K^1$ representatives on even dimensional manifolds, which should
be of independent interests. For example, it gives an intrinsic interpretation
of the so called Wess-Zumino term in the WZW theory in physics.
