Periods of principal homogeneous spaces of algebraic tori

A generic torsor of an algebraic torus S over a field F is the generic fiber of a S-torsor P → T, where P is a quasi-trivial torus containing S as a subgroup and T = P/S. The period of a generic S-torsor over a field extension K/F, i.e., the order of the class of the torsor in the group H ^p1(K, S) does not depend on the choice of a generic torsor. In the paper we compute the period of a generic torsor of S in terms of the character lattice of the torus S.