To co-opt something is to take possession of it to use it for your own purposes. Don't co-opt your friend's short story title — take the time to come up with your own!
When you co-opt an idea, you use it as though you'd come up with it, despite the fact that someone else thought of it first. Politicians often do this, as when they co-opt a rival's popular positions or policies. Another way to use this word is to mean "appoint or elect to a committee." The Latin root, cooptare, means "to choose as a colleague or member of one's tribe."