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We exploit various inclusions of algebraic groups to give a new constructionof groups of type E8, determine the Killing forms of the resulting E8's, anddefine an invariant of central simple algebras of degree 16 with orthogonalinvolution "in I^3", equivalently, groups of type D8 with a half-spinrepresentation defined over the base field. The determination of the Killingform is done by restricting the adjoint representation to various twisted formsof PGL2 and requires very little computation.  An appendix by Kirill Zainoulline contains a type of "index reduction" resultfor groups of type D.

Orthogonal involution on algebras of degree 16 and the Killing form of E8