Brodzki, J.Varghese, M.Rosenberg, J.Szabo, R.2008-01-152008-01-152008Communications in Mathematical Physics, 2008; 277(3):643-7060010-36161432-0916http://hdl.handle.net/2440/40234The original publication is available at www.springerlink.comWe develop some of the ingredients needed for string theory on noncommutative spacetimes, proposing an axiomatic formulation of T-duality as well as establishing a very general formula for D-brane charges. This formula is closely related to a noncommutative Grothendieck-Riemann-Roch theorem that is proved here. Our approach relies on a very general form of Poincaré duality, which is studied here in detail. Among the technical tools employed are calculations with iterated products in bivariant -theory and cyclic theory, which are simplified using a novel diagram calculus reminiscent of Feynman diagrams.enJournal article00200800182008011511120410.1007/s00220-007-0396-y0002516500000032-s2.0-3744900186843952Varghese, M. [0000-0002-1100-3595]