Cohomological invariants play an important role in the classification of G-torsors, where G is an algebraic group over a field. However these invariants are hard to compute. In case of a Weyl group G they have been recently computed (with some restrictions on the base field). A crucial role in this computation is played by a splitting principle, which roughly says that an invariant of a Weyl group is determined by its restriction to elementary abelian 2-subgroups generated by reflections. In the talk I will discuss the generalization of this principle to orthogonal reflection groups. (joint work with Christian Hirsch)