  We consider spatial discretizations by the finite section method of the
restricted group algebra of a finitely generated discrete group, which is
represented as a concrete operator algebra via its left-regular representation.
Special emphasis is paid to the quasicommutator ideal of the algebra generated
by the finite sections sequences and to the stability of sequences in that
algebra. For both problems, the sequence of the discrete boundaries plays an
essential role. Finally, for commutative groups and for free non-commutative
groups, the algebras of the finite sections sequences are shown to be fractal.
