  We present the results of the first study of global oscillations of
relativistic stars with both elastic crusts and interpenetrating superfluid
components. For simplicity, we focus on the axial quasi-normal modes. Our
results demonstrate that the torsional crust modes are essentially unaffected
by the coupling to the gravitational field. This is as expected since these
oscillations are known to be weak gravitational-wave sources. In contrast, the
presence of a loosely coupled superfluid neutron component in the crust can
have a significant effect on the oscillation spectrum. We show that the
entrainment between the superfluid and the crust nuclei is a key parameter in
the problem. Our analysis highlights the need for a more detailed understanding
of the coupled crust-superfluid at the microphysical level. Our numerical
results have, even though we have not considered magnetised stars, some
relevance for efforts to carry out seismology based on quasi-periodic
oscillations observed in the tails of magnetar flares. In particular, we argue
that the sensitive dependence on the entrainment may have to be accounted for
in attempts to match theoretical models to observational data.
