  The polarization properties of the elastic electron scattering on H-like ions
are investigated within the framework of the relativistic QED theory. The
polarization properties are determined by a combination of relativistic effects
and spin exchange between the incident and bound electrons. The scattering of a
polarized electron on an initially unpolarized ion is fully described by five
parameters. We study these parameters for non-resonant scattering, as well as
in the vicinity of LL resonances, where scattering occurs through the formation
and subsequent decay of intermediate autoionizing states. The study was carried
out for ions from $\txt{B}^{4+}$ to $\txt{Xe}^{53+}$. Special attention was
paid to the study of asymmetry in electron scattering.
