  We generalize the first author's construction of intersection spaces to the
case of stratified pseudomanifolds of stratification depth 1 with twisted link
bundles, assuming that each link possesses an equivariant Moore approximation
for a suitable choice of structure group. As a by-product, we find new
characteristic classes for fiber bundles admitting such approximations. For
trivial bundles and flat bundles whose base has finite fundamental group these
classes vanish. For oriented closed pseudomanifolds, we prove that the reduced
rational cohomology of the intersection spaces satisfies global Poincar\'e
duality across complementary perversities if the characteristic classes vanish.
The signature of the intersection spaces agrees with the Novikov signature of
the top stratum. As an application, these methods yield new results about the
Goresky-MacPherson intersection homology signature of pseudomanifolds. We
discuss several nontrivial examples, such as the case of flat bundles and
symplectic toric manifolds.
