Let G be a group, ZG and QG be the integral and rational group ring. A known theorem due to Swan states that if G is a finite group and P a finitely generated projective ZG-module, the rationalization P ⊗ Q is free as a QG-module. There have been many attempts to generalize Swan’s theorem to infinite groups, notably the Bass trace conjectures. Lück and Reich formulated what is known as the integral K_0(ZG)-to-K_0(QG)-conjecture, which states that the map induced by rationalization from K_0(ZG) to K_0(QG) has image only in the subgroup of K_0(QG) generated by the free modules. We show that the integral K_0(ZG)-to-K_0(QG)-conjecture is false by constructing concrete counterexamples via amalgamated products of groups K and H, which allow particular quaternionic representations.