The kernel of the Rost invariant, Serre's conjecture II and the Hasse principle for quasi-split groups \(^{3,6}D_4\), \(E_6\), \(E_7\).
For the simple simply connected groups in the title defined over a perfect field of characteristic \(\neq 2,3\), it is proved: the kernel of the Rost invariant is trivial; if \(\text{cd\,}F\leq 2\) then Serre's conjecture II holds.
scientific article; zbMATH DE number 1982572