  Co lombeau's construction of generalized functions (in its special variant)
is extended to a theory of generalized sections of vector bundles. As
particular cases, generalized tensor analysis and exterior algebra are studied.
A point value characterization for generalized functions on manifolds is
derived, several algebraic characterizations of spaces of generalized sections
are established and consistency properties with respect to linear
distributional geometry are derived. An application to nonsmooth mechanics
indicates the additional flexibility offered by this approach compared to the
purely distributional picture.
