  We study the vacuum polarization effects associated with a massive fermionic
field in a spacetime produced by a global monopole considering a nontrivial
inner structure for it. In the general case of the spherically symmetric static
core with finite support we evaluate the vacuum expectation values of the
energy-momentum tensor and the fermionic condensate in the region outside the
core. These quantities are presented as the sum of point-like global monopole
and core-induced contributions. The asymptotic behavior of the core-induced
vacuum densities are investigated at large distances from the core, near the
core and for small values of the solid angle corresponding to strong
gravitational fields. As an application of general results the flower-pot model
for the monopole's core is considered and the expectation values inside the
core are evaluated.
