  We construct the teleparallel dynamics for extended geometry where the
structure algebra is (an extension of) an untwisted affine Kac-Moody algebra.
This provides a geometrisation of the Geroch symmetry appearing on dimensional
reduction of a gravitational theory to two dimensions. The formalism is adapted
to the underlying tensor hierarchy algebra, and will serve as a stepping stone
towards the geometrisation of other infinite-dimensional, e.g. hyperbolic,
symmetries.
