A wonderful embedding of the loop group

I describe the wonderful compactification of loop groups. These compactifications are obtained by adding normal-crossing boundary divisors to the group LG of loops in a reductive group G (or more accurately, to the semi-direct product C×⋉LG) in a manner equivariant for the left and right C×⋉LG-actions. The analogue for a torus group T is the theory of toric varieties; for an adjoint group G, this is the wonderful compactification of De Concini and Procesi. The loop group analogue is suggested by work of Faltings in relation to the compactification of moduli of G-bundles over nodal curves.