Motivic cycles on K3 double covers of del Pezzo surfaces

In this paper we construct indecomposable motivic cycles in the group $H^3_{\mathcal M}({\tilde{Z}},{\mathbb{Q}}(2)$ where ${\tilde{Z}}$ is a $K3$ surface obtained as a branched double cover of a del Pezzo surface. The cycles are constructed using $(-1)$ curves on the del Pezzo and is a generalization of a recent paper of Ma and Sato [11].