  I construct a model of the inner crust of neutron stars using interactions
from chiral effective field theory (EFT) in order to calculate its equation of
state (EOS), shear properties, and the spectrum of crustal shear modes. I
systematically study uncertainties associated with the nuclear physics input,
the crust composition, and neutron entrainment, and estimate their impact on
crustal shear properties and the shear-mode spectrum. I find that the
uncertainties originate mainly in two sources: The neutron-matter EOS and
neutron entrainment. I compare the spectrum of crustal shear modes to observed
frequencies of quasi-periodic oscillations in the afterglow of giant
$\gamma$-ray bursts and find that all of these frequencies could be described
within uncertainties, which are, however, at present too sizable to infer
neutron-star properties from observations.
