Problems in $R$-equivalence of semisimple groups

$R$-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.