  We report a study of the Aharonov-Bohm effect, the oscillations of the
resistance of a mesoscopic ring as a function of a perpendicular magnetic
field, in a GaAs two-dimensional hole system with a strong spin-orbit
interaction. The Fourier spectra of the oscillations reveal extra structure
near the main peak whose frequency corresponds to the magnetic flux enclosed by
the ring. A comparison of the experimental data with results of simulations
demonstrates that the origin of the extra structure is the geometric (Berry)
phase acquired by the carrier spin as it travels around the ring.
