Geodesic
Problems in $R$-equivalence of semisimple groups
Zapiski Nauchnykh Seminarov POMI, Algebraic numbers and finite groups, Tome 86 (1979), pp. 49-65

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$R$-equivalence on the unimodular group of a simple algebra is studied in detail. A rather complete characterization is obtained for the $R$-equivalence group of semisimple groups over the field of $\rho$-adic numbers. In this case all the Manin groups are commutative, and for simply connected groups, they are trivial. It is shown how $R$-equivalence can be applied to the weak approximation problem. 
@article{ZNSL_1979_86_a6,
     author = {V. E. Voskresenskii},
     title = {Problems in $R$-equivalence of semisimple groups},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {49--65},
     publisher = {mathdoc},
     volume = {86},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_86_a6/}
}
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V. E. Voskresenskii. Problems in $R$-equivalence of semisimple groups. Zapiski Nauchnykh Seminarov POMI, Algebraic numbers and finite groups, Tome 86 (1979), pp. 49-65. http://geodesic.mathdoc.fr/item/ZNSL_1979_86_a6/