We introduce SPOT, an object-centric imitation learning framework. The key idea is to capture each task by an object-centric representation, specifically the SE(3) object pose trajectory relative to the target. This approach decouples embodiment actions from sensory inputs, facilitating learning from various demonstration types, including both action-based and action-less human hand demonstrations, as well as cross-embodiment generalization. Additionally, object pose trajectories inherently capture planning constraints from demonstrations without the need for manually-crafted rules.