Abstract :
Assume that X is a compact connected orientable nonsingular real algebraic variety with an algebraic free S1-action so that the quotient Y=X/S1 is also a real algebraic variety. If π : X→Y is the quotient map then the induced map between reduced algebraic K-groups, tensored with image, image is onto, where image, image denoting the ring of entire rational (regular) functions on the real algebraic variety X, extending partially the Bochnak–Kucharz result that image for any real algebraic variety X. As an application we will show that for a compact connected Lie group G image.
