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We study affine Grassmannians for ramified triality groups. These groups areof type ${}^3D_4$, so they are forms of the orthogonal or the spin groups in 8variables. They can be given as automorphisms of certain twisted compositionalgebras obtained from the octonion algebra. Using these composition algebras,we give descriptions of the affine Grassmannians for these triality groups asfunctors classifying suitable lattices in a fixed space.

Affine Grassmannians for Triality Groups