We plan to begin with an overview of classical Riemann-Roch formulas in homotopic topology and algebraic geometry. Then we will give an introduction to Gromov-Witten invariants and study in detal general properties of such invariants in genus 0. At this point we will have to develop the so-called "symplectic loop space formalism" - a combinatorial framework (replacing the notion of Frobenius structures) suitable for comparing Gromov-Witten invariants of various sorts. Our intermediate goal will be to establish a number of general "twisting" formulas (they typically show that various attempts to invent new GW-invariants are unsuccessful, by expressing those new invariants in terms of the old ones), including the Quantum Hirzebruch-Riemann-Roch formula of Tom Coates, expressing certain GW-invariants with values in complex cobordisms in terms of cohomologica ones. We'll conclude with proving the title theorem, providing some applications (among them - the intrinsic role of finite-difference equations in quantum K-theory), and outlining a number of open problems and directions promising for further research. Prerequisites: For courses of this level, I used to write: A dense subset in Griffitth-Harris' "Principles of Algebraic Geometry", but then somebody added in handwriting: ... in discrete topology. Well, the truth is, that by now I myself have so firmly forgotten those Principles, that saying "a nowhere dense set" (in that topology) would be more appropriate.