  Let W be the Weyl group of a crystallographic root system acting on the
associated weight lattice by reflections. In the present notes we extend the
notion of an exponent of the W-action introduced in [Baek-Neher-Zainoulline,
arXiv:1106.4332] to the context of an arbitrary algebraic oriented cohomology
theory of Levine-Morel, Panin-Smirnov and the associated formal group law. From
this point of view the classical Dynkin index of the associated Lie algebra
will be the second exponent of the deformation map from the multiplicative to
the additive formal group law. We apply this generalized exponent to study the
torsion part of an arbitrary oriented cohomology theory of a twisted flag
variety.
