  It is well known that every word hyperbolic group has a well-defined visual
boundary. An example of C. Croke and B. Kleiner shows that the same cannot be
said for CAT(0) groups. All boundaries of a CAT(0) group are, however, shape
equivalent, as observed by M. Bestvina and R. Geoghegan. Bestvina has asked if
they also satisfy the stronger condition of being cell-like equivalent. This
article describes a construction which will produce CAT(0) groups with multiple
boundaries. These groups have very complicated boundaries in high dimensions.
It is our hope that their study may provide insight into Bestvina's question.
