As user6591 notes, the Shulchan Aruch (OC 123:5) says that the prayer leader does not need to take three steps backward after his repetition of the amida, and the Mishna B'rura (:18) gives the reason: "because he relies on the steps of the kadish" (kadish shalem, also called kadish "Tiskabel").
But in many congregations, on weekdays, a new leader starts leading the services before that kadish. (Typically in my experience, he starts with "Ashre".) And someone not saying kadish doesn't take steps during it. Thus, the one who repeated the amida seemingly doesn't take any steps after it. What should he do?
Some possibilities that come to mind:
- He should take three steps back whenever he wants.
- He should take three steps back immediately after the repetition, since, after all, why wait?
- He should not take three steps back: they were never instituted for the repetition.
- He should take three steps back when the new leader does, viz while listening to kadish shalem.
- He should take three steps back when he leaves the service-leadership, since that's his leavetaking time.
- If he's saying kadish yasom or kadish d'rabanan toward the end of the prayer service, the steps he's taking in that kadish count for the amida repetition also.
- He should specifically say kadish yasom or kadish d'rabanan toward the end of the prayer service in order to take three steps during that kadish.
I welcome a good argument or source for any of these or any other answer.