  A semiclassical approximation for the matrix elements of a quantum chaotic
propagator in the scar function basis has been derived. The obtained expression
is solely expressed in terms of canonical invariant objects. For our purpose,
we have used, the recently developed, semiclassical matrix elements of the
propagator in coherent states, together with the linearization of the flux in
the neighborhood of a classically unstable periodic orbit of chaotic two
dimensional systems. The expression here derived is successfully verified to be
exact for a (linear) cat map, after the theory is adapted to a discrete phase
space appropriate to a quantized torus.
