  For For a given PDE system, or an exterior differential system possessing a
Lie group of internal symmetries the orbit reduction procedure is introduced.
It is proved that the solutions of the reduced exterior differential system are
in one-to-one correspondence with the moduli space of regular solutions of the
prolongation of the original system.
  The isomorphism between the local characteristic cohomology of the reduced
unconstrained jet space and the Lie algebra cohomology of the symmetry group is
established.
  The group-invariant Euler-Lagrange equations of an invariant variational
problem are described as a composition of the Euler-Lagrange operators on the
reduced jet space and certain other differential operators on the reduced jet
space. The practical algorithm of computing these operators is given.
