  We investigate the vacuum expectation values for the energy-momentum tensor
of a massive scalar field with general curvature coupling and obeying the Robin
boundary condition on a spherical shell in the $D+1$-dimensional global
monopole background. The expressions are derived for the Wightman function, the
vacuum expectation values of the field square, the vacuum energy density,
radial and azimuthal stress components in both regions inside and outside the
shell. A regularization procedure is carried out by making use of the
generalized Abel-Plana formula for the series over zeros of cylinder functions.
This formula allows us to extract from the vacuum expectation values the parts
due to the global monopole gravitational field in the situation without a
boundary, and to present the boundary induced parts in terms of exponentially
convergent integrals, useful, in particular, for numerical calculations. The
asymptotic behavior of the vacuum densities is investigated near the sphere
surface and at large distances. We show that for small values of the parameter
describing the solid angle deficit in global monopole geometry the boundary
induced vacuum stresses are strongly anisotropic.
