This is with an understanding on normalization (cf. Voskresenskii book Ch. 5); in any case the conjecture was of the value in this case. (Here simply connected has the usual meaning for algebraic group theory, of not having a proper algebraic covering, which is not exactly the topologists' meaning in all cases.)
K. F. Lai (1980) extended the class of known cases to quasisplit reductive groups. proved it for all groups satisfying the Hasse principle, which at the time was known for all groups without E8 factors. V. I. Chernousov (1989) removed this restriction, by proving the Hasse principle for the resistant E8 case (see strong approximation in algebraic groups), thus completing the proof of Weil's conjecture.