Geodesic
Birational properties of linear algebraic groups
Izvestiya. Mathematics , Tome 4 (1970) no. 1, pp. 1-17

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This paper investigates the question of birational equivalence of linear algebraic groups. Certain necessary conditions are derived for rationality of a group over the field of definition, which in application to algebraic tori are fairly delicate. In particular, it is shown that the condition $\textrm{Ш}(G)=0$ is a necessary criterion of rationality for tori and for semisimple groups defined over an algebraic number field. 
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     author = {V. E. Voskresenskii},
     title = {Birational properties of linear algebraic groups},
     journal = {Izvestiya. Mathematics },
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V. E. Voskresenskii. Birational properties of linear algebraic groups. Izvestiya. Mathematics , Tome 4 (1970) no. 1, pp. 1-17. http://geodesic.mathdoc.fr/item/IM2_1970_4_1_a0/