  The BRST structure of the extended Bondi-Metzner-Sachs symmetry group of
asymptotically flat manifolds is investigated using the recently introduced
framework of the Beltrami field parametrization of four-dimensional metrics.
The latter identifies geometrically the two physical degrees of freedom of the
graviton as fundamental fields. The graded BRST BMS4 nilpotent differential
operator relies on four horizontality conditions giving a Lagrangian
reformulation of the asymptotic BMS4 symmetry. A series of cocycles is found
which indicate the possibility of anomalies for three-dimensional Lagrangian
theories to be built in the null boundaries of asymptotically flat spaces from
the principle of BRST BMS4 invariance.
