  A general framework for a systematic quasi-localization of canonical general
relativity and a new ingredient, the requirement of the gauge invariance of the
boundary terms appearing in the calculation of Poisson brackets, are given. As
a consequence of this it is shown, in particular, that the generator vector
fields (built from the lapse and shift) of the quasi-local quantities must be
divergence free with respect to a Sen-type connection; and the volume form
induced from the spatial metric on the boundary surface must be fixed.
