Abstract Generalized planning is concerned with the characterization and computation of plans that solve many instances at once. In the standard formulation, a generalized plan is a mapping from feature or observation histories into actions, assuming that the instances share a common pool of features and actions. This assumption, however, excludes the standard relational planning domains where actions and objects change across instances. In this work, we extend the standard formulation of generalized planning to such domains. This is achieved by projecting the actions over the features, resulting in a common set of abstract actions which can be tested for soundness and completeness, and which can be used for generating general policies such as “if the gripper is empty, pick the clear block above x and place it on the table” that achieve the goal clear(x) in any Blocksworld instance. In this policy, “pick the clear block above x” is an abstract action that may represent the action Unstack(a, b) in one situation and the action Unstack(b, c) in another. Transformations are also introduced for computing such policies by means of fully observable non-deterministic (FOND) planners. The value of generalized representations for learning general policies is also discussed.