Found the right component to use. svenmeier pushed me vaguely in the right direction but this should be done at the question marks:
List<Action> available = dao.getAllActions();
form.add(new CheckBoxMultipleChoice<Action>(actions, available));
To properly render the string I added a ChoiceRender to the CheckBoxMultipleChoice:
new ChoiceRenderer<Action>() {
@Override
public Object getDisplayValue(Action object) {
return object.getDisplayName(); //return any string describing the object
}
}