Given a manifold 
with boundary 
, and isometry 
, for each subgroup 
of one can form the crossed product C*-algebra 
. This post is a one in a series of posts that investigates the non-commutative analogues of the Mostow rigidity theorem, which shows that for certain locally symmetric spaces the fundamental group is a complete isomorphism (i.e. isometry) invariant for the locally symmetric spaces, setteling the Borel conjecture for such spaces.
In this post we look at the failure of the theorem in the special case of 
.