  Using a Lax pair based on twisted affine $sl(2,R)$ Kac-Moody and Virasoro
algebras, we deduce a r-matrix formulation of two dimensional reduced vacuum
Einstein's equations. Whereas the fundamental Poisson brackets are
non-ultralocal, they lead to pure c-number modified Yang-Baxter equations. We
also describe how to obtain classical observables by imposing reasonable
boundaries conditions.
