Making informed driving decisions requires reliable prediction of other vehicles' trajectories. In this paper, we present a novel learned multi-modal trajectory prediction architecture for automated driving. It achieves kinematically feasible predictions by casting the learning problem into the space of accelerations and steering angles -by performing action-space prediction, we can leverage valuable model knowledge. Additionally, the dimensionality of the action manifold is lower than that of the state manifold, whose intrinsically correlated states are more difficult to capture in a learned manner. For the purpose of action-space prediction, we present the simple Feed-Forward Action-Space Prediction (FFW-ASP) architecture. Then, we build on this notion and introduce the novel Self-Supervised Action-Space Prediction (SSP-ASP) architecture that outputs future environment context features in addition to trajectories. A key element in the self-supervised architecture is that, based on an observed action history and past context features, future context features are predicted prior to future trajectories. The proposed methods are evaluated on real-world datasets containing urban intersections and roundabouts, and show accurate predictions, outperforming state-of-the-art for kinematically feasible predictions in several prediction metrics.