  We present an analysis of the Aharonov-Bohm oscillations for a mesoscopic
ring with a quantum dot inserted in one of its arms. It is shown that
microreversibility demands that the phase of the Aharonov-Bohm oscillations
changes {\it abruptly} when a resonant level crosses the Fermi energy. We use
the Friedel sum rule to discuss the conservation of the parity of the
oscillations at different conductance peaks. Our predictions are illustrated
with the help of a simple one channel model that permits the variation of the
potential landscape along the ring.
