We have experimentally investigated Aharonov-Bohm conductance oscillat
ions in two-dimensional tings in the presence of a strong Rashba spin-
orbit interaction. The peak of the ensemble average spectrum correspon
ding to the h/e oscillations is split in several samples. We argue tha
t the splitting originates from the geometric phase acquired by an ele
ctron spin under the influence of the spinorbit interaction. Our resul
ts demonstrate how the ensemble average spectrum provides information
otherwise not easily accessible.