Knot reversal and rational concordance

We give an infinite family of knots that are not rationally concordant to their reverses. More precisely, if R denotes the involution of the rational knot concordance group QC induced by string reversal and Fix(R) denotes the subgroup of knots fixed under R in QC, then QC/Fix(R) contains an infinite rank subgroup. As a corollary, we show that there exists a knot K such that for every pair of coprime integers p and q, the (p,q)-cable of K is not concordant to the reverse of the (p,q)-cable of K.