Throughout this paper, k denotes a field of characteristic 0. We write E8 for the split simple algebraic group with Killing-Cartan type E8. The Galois cohomology set H (k, E8) classifies simple algebraic groups of type E8 over k. One of the goals of the theory of algebraic groups over arbitrary fields is to understand the groups of type E8, equivalently, understand the set H(k, E8). The main to...