  We apply the methods of homology and K-theory for branes wrapping spaces
stratified fibered over hyperbolic orbifolds. In addition, we discuss the
algebraic K-theory of any discrete co-compact Lie group in terms of appropriate
homology and Atiyah-Hirzebruch type spectral sequence with its non-trivial lift
to K-homology. We emphasize the fact that the physical D-branes properties are
completely transparent within the mathematical framework of K-theory. We derive
criteria for D-brane stability in the case of strongly virtually negatively
curved groups. We show that branes wrapping spaces stratified fibered over
hyperbolic orbifolds carry charge structure and change the additive structural
properties in K-homology.
