  It is well-known that every algebraic group of type F_4 is the automorphism
group of an exceptional Jordan algebra, and that up to isogeny all groups of
type ^1E_6 with trivial Tits algebras arise as the isometry groups of norm
forms of such Jordan algebras. We describe a similar relationship between
groups of type E_6 and groups of type E_7 and use it to give explicit
descriptions of the homogeneous projective varieties associated to groups of
type E_7 with trivial Tits algebras. The underlying algebraic structure for the
relationship considered here are a sort of 56-dimensional structurable algebra
which are forms of an algebra constructed from an exceptional Jordan algebra.
