Title: A torsion projective class for a group algebra Author: Ian J. Leary AMS numbers: 19A31, also 16S34 and 55N15. Author's address: Faculty of Mathematical Sciences, University of Southampton, Southampton, SO17 1BJ. Abstract: For a certain cyclic-by-finite group, we construct an element of order two in the algebraic $K_0$ of the rational group ring, whose image in $K_0$ of the complex group ring is zero. Non-triviality of the element is established using topological methods. To appear in Bull. London Math. Soc.