Let $S(N)$ be a random walk on a countable abelian group$G$ which acts on a probability space $E$ by measure-preservingtransformations$(T_v)_{v\in G}$. For any $\Lambda \subset E$ we consider the random return time$\tau$ at which $T_{S(\tau)}\in\Lambda$. We show that the corresponding inducedskew product transformation is K-mixing whenever a natural subgroup of$G$ acts ergodically on $E$.