  The vacuum expectation values of the energy--momentum tensor and the
fermionic condensate are analyzed for a massive spinor field obeying the MIT
bag boundary condition on a cylindrical shell in the cosmic string spacetime.
Both regions inside and outside the shell are considered. By applying to the
corresponding mode-sums a variant of the generalized Abel--Plana formula, we
explicitly extract the parts in the expectation values corresponding to the
cosmic string geometry without boundaries. In this way the renormalization
procedure is reduced to that for the boundary-free cosmic string spacetime. The
parts induced by the cylindrical shell are presented in terms of integrals
rapidly convergent for points away from the boundary. The behavior of the
vacuum densities is investigated in various asymptotic regions of the
parameters. In the limit of large values of the planar angle deficit, the
boundary-induced expectation values are exponentially suppressed. As a special
case, we discuss the fermionic vacuum densities for the cylindrical shell on
the background of the Minkowski spacetime.
