  We show that an outer action of a finite abelian group on a simple
Cuntz-Krieger algebra is strongly approximately inner in the sense of Izumi if
the action is given by diagonal quasi-free automorphisms and the associated
matrix is aperiodic. This is achieved by an approximate cohomology
vanishing-type argument for the canonical shift restricted to the relative
commutant of the set of domain projections of the canonical generating
isometries in the fixed point algebra.
