  In the present notes we generalize the classical work of Demazure [Invariants
sym\'etriques entiers des groupes de Weyl et torsion] to arbitrary oriented
cohomology theories and formal group laws. Let G be a split semisemiple linear
algebraic group over a field and let T be its split maximal torus. We construct
a generalized characteristic map relating the so called formal group ring of
the character group of T with the cohomology of the variety of Borel subgroups
of G. The main result of the paper says that the kernel of this map is
generated by W-invariant elements, where W is the Weyl group of G. As one of
the applications we provide an algorithm (realized as a Macaulau2 package)
which can be used to compute the ring structure of an oriented cohomology
(algebraic cobordism, Morava $K$-theories, connective K-theory, Chow groups,
K_0, etc.) of a complete flag variety.
