An Exceptional geometry for D = 11 supergravity?

We analyse the algebraic constraints of the generalized vielbein in SO(1,2)×SO(16) invariant d = 11 supergravity, and show that the bosonic degrees of freedom of d = 11 supergravity, which become the physical ones upon reduction to d = 3, can be assembled into an E8(8)-valued vielbein already in 11 dimensions. A crucial role in the construction is played by the maximal nilpotent commuting subalgebra of E8(8), of dimension 36, suggesting a partial unification of general coordinate and tensor gauge transformations.