  There is a gap that has been left open since the formulation of general
relativity in terms of Ashtekar's new variables namely the treatment of
asymptotically flat field configurations that are general enough to be able to
define the generators of the Lorentz subgroup of the asymptotical Poincar\'e
group. While such a formulation already exists for the old geometrodynamical
variables, up to now only the generators of the translation subgroup could be
defined because the function spaces of the fields considered earlier are taken
too special. The transcription of the framework from the ADM variables to
Ashtekar's variables turns out not to be straightforward due to the a priori
freedom to choose the internal SO(3) frame at spatial infinity and due to the
fact that the non-trivial reality conditions of the Ashtekar framework reenter
the stage when imposing suitable boundary conditions on the fields and the
Lagrange multipliers.
