Given positive integers n and m, we consider dynamical systems in which n
copies of a topological space is homeomorphic to m copies of that same space.
The universal such system is shown to arise naturally from the study of a
C*-algebra we denote by O_{mn}, which in turn is obtained as a quotient of the
well known Leavitt C*-algebra L_{mn}, a process meant to transform the
generating set of partial isometries of L{mn} into a tame set. Describing
O_{mn} as the crossed-product of the universal (m,n)-dynamical system by a
partial action of the free group F_{m+n}, we show that O_{mn} is not exact when
n and m are both greater than or equal to 2, but the corresponding reduced
crossed-product, denoted O_{mn}^r, is shown to be exact and non-nuclear. Still
under the assumption that m,n>=2, we prove that the partial action of F_{m+n}
is topologically free and that O_{mn}^r satisfies property (SP) (small
projections). We also show that O_{mn}^r admits no finite dimensional
representations. The techniques developed to treat this system include several
new results pertaining to the theory of Fell bundles over discrete groups.Comment: 38 page
