For such a basic intention, I’ve found a pretty complicated way which has it’s side effects:
I’ve split the action into two parts by first duplicating it, deleting the second part from the first action and the first part from the second action. As Blender cannot edit actions as such w/o being assigned to something (like with everything else in Blender), you first have to assign one action to the object, edit it, press the [F] button to add a fake user - Blender still deletes things by itself without asking - select the other action and edit that one. Then make an NLA track/strip from the first action, add another clip referring to the second action… Can you still follow? Well, it doesn’t matter as it’s not an acceptable workflow anyway. One side effect is that the last key frame of one action is equal to the first key frame of the second action, and whenever you change one, you have to keep in mind for your whole live that you need to perform the same modification to the first key frame of the second action.
Ok, back to practice. Simple requirement, simple answer: How can I repeat only a part of an action infinitely?