We prove the stable rationality of almost simple adjoint algebraic groups, the connected components of the Dynkin diagram of anisotropic kernel of which contain at most two vertices. The (stable) rationality of many isotropic almost simple groups with small anisotropic kernel and some related results over arbitrary fields are discussed.
"Rationality of almost simple algebraic groups." J. Math. Kyoto Univ. 39 (1) 185 - 202, 1999. https://doi.org/10.1215/kjm/1250517958