  We study theoretically the effect of spin-orbit coupling on quantum well
excitons in a strong magnetic field. We show that, in the presence of an
in-plane field component, the excitonic absorption spectrum develops a
double-peak structure due to hybridization of bright and dark magnetoexcitons.
If the Rashba and Dresselhaus spin-orbit constants are comparable, the
magnitude of splitting can be tuned in a wide interval by varying the azimuthal
angle of the in-plane field. We also show that the interplay between spin-orbit
and Coulomb interactions leads to an anisotropy of exciton energy dispersion in
the momentum plane. The results suggest a way for direct optical measurements
of spin-orbit parameters.
