Degree 4 cohomological invariants of algebraic tori

In this paper, we determine the motive of the classifying torsor of an algebraic torus. As a result, we give an exact sequence describing the degree 4 cohomological invariants of algebraic tori. Using results by Blinstein and Merkurjev, this provides a formula for the degree 4 unramified cohomology group of an algebraic torus, via a flasque resolution.