  A noncommutative-geometric generalization of classical Weil theory of
characteristic classes is presented, in the conceptual framework of quantum
principal bundles. A particular care is given to the case when the bundle does
not admit regular connections. A cohomological description of the domain of the
Weil homomorphism is given. Relations between universal characteristic classes
for the regular and the general case are analyzed. In analogy with classical
geometry, a natural spectral sequence is introduced and investigated. The
appropriate counterpart of the Chern character is constructed, for structures
admitting regular connections. Illustrative examples and constructions are
presented.
