### Invariants, torsion indices and oriented cohomology of complete flags, by Baptiste Calmes, Victor Petrov, and Kirill Zainoulline

In the present notes we generalize the classical work of Demazure [Invariants
symetriques entiers des groupes de Weyl et torsion] to arbitrary oriented
cohomology theories and formal group laws.

Let G be a split semisimple 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 Macaulay2
package) which can be used to compute the ring structure of an oriented
cohomology (algebraic cobordism of Levine-Morel, Morava K-theories, connective
K-theory, Chow groups, etc.) of a complete flag variety.

Baptiste Calmes <baptiste.calmes@univ-artois.fr>

Victor Petrov <victorapetrov@googlemail.com>

Kirill Zainoulline <kirill@uottawa.ca>