On R-triviality of F 4
Israel Journal of Mathematics
It is known that simple algebraic groups of type F4 defined over a field k are precisely the full automorphism groups of Albert algebras over k. We explore R-triviality for the algebraic group Aut(A) when A is an Albert algebra. In this paper, we consider the case when A arises from the first Tits construction. We prove that Aut(A) is R-trivial, in the sense of Manin.
Thakur, Maneesh, "On R-triviality of F 4" (2021). Journal Articles. 1815.