  Question 2.6 of Bestvina's Questions in Geometric Group Theory asks whether
every pair of boundaries of a given CAT(0) group G is cell-like equivalent. The
question was posed by Bestvina shortly after the discovery, by Croke and
Kleiner, of a CAT(0) group that admits multiple boundaries. Previously, it had
been observed by Bestvina and Geoghegan that all boundaries of a torsion free
CAT(0) G would necessarily have the same shape. Since "cell-like equivalence"
is weaker than topological equivalence, but in most circumstances, stronger
(and more intuitive) than shape equivalence, this question is a natural one
when working with the pathological types of spaces that occur as group
boundaries. Furthermore, the definition of cell-like equivalence allows for a
obvious G-equivariant extension.
  In this paper we provide a positive answer to Bestvina's G-equivariant
Cell-like Equivalence Question for the class of admissible groups studied by
Croke and Kleiner in 2002. Since that collection includes the original
Croke-Kleiner group, our result provides a strong solution to Q2.6, for the
group that originally motivated the question.
