Suppose that G is an absolutely almost simple simply connected algebraic group over a field k. The Rost invariant associates an element a(P) of the Galois cohomology group H3(k,Q/Z(2)) to a G-torsor P. The element a(P) is constructed as follows.
Choose a finite extension K of k such that G splits over K and P has a rational point over K. Then the exact sequence splits canonically as a direct sum so the étale cohomology group contains Q/Z canonically.
The invariant a(P) is the image of the element 1/[K:k] of Q/Z under the trace map from H3et(PK,Q/Z(2)) to H3et(P,Q/Z(2)), which lies in the subgroup H3(k,Q/Z(2)).
These invariants a(P) are functorial in field extensions K of k; in other words the fit together to form an element of the cyclic group Inv3(G,Q/Z(2)) of cohomological invariants of the group G, which consists of morphisms of the functor K→H1(K,G) to the functor K→H3(K,Q/Z(2)).
This element of Inv3(G,Q/Z(2)) is a generator of the group and is called the Rost invariant of G.