  We investigate exceptional generalised diffeomorphisms based on $E_{8(8)}$ in
a geometric setting. The transformations include gauge transformations for the
dual gravity field. The surprising key result, which allows for a development
of a tensor formalism, is that it is possible to define field-dependent
transformations containing connection, which are covariant. We solve for the
spin connection and construct a curvature tensor. A geometry for the Ehlers
symmetry SL(n+1) is sketched. Some related issues are discussed.
