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We apply the methods of homology and K-theory for branes wrapping spacesstratified fibered over hyperbolic orbifolds. In addition, we discuss thealgebraic K-theory of any discrete co-compact Lie group in terms of appropriatehomology and Atiyah-Hirzebruch type spectral sequence with its non-trivial liftto K-homology. We emphasize the fact that the physical D-branes properties arecompletely transparent within the mathematical framework of K-theory. We derivecriteria for D-brane stability in the case of strongly virtually negativelycurved groups. We show that branes wrapping spaces stratified fibered overhyperbolic orbifolds carry charge structure and change the additive structuralproperties in K-homology.

D-Branes on Spaces Stratified Fibered Over Hyperbolic Orbifolds