  We propose to unify the Gravity and Standard Model gauge groups by using
algebraic spinors of the standard four-dimensional Clifford algebra, in
left-right symmetric fashion. This generates exactly a Standard Model family of
fermions, and a Pati-Salam unification group emerges, at the Planck scale,
where (chiral) self-dual gravity decouples. As a remnant of the unification,
isospin-triplets spin-two particles may naturally appear at the weak scale,
providing a striking signal at the LHC.
