Is the chazzan required to take three steps back after completing chazaras hashatz?
The chazzan does not have to take three steps back after completing chazoras hashatz. The reason for this is because the three steps that he will take after saying kaddish liskabel are considered his three steps. As a side point, the poskim say that since the chazzan’s three steps after chazoras hashatz are done after kaddish tibkabel, which is said after “ova l’zion”, the chazzan should be careful not to talk out unnecessarily until then.
There are instances when the chazzan however should take the three steps back after chazoras hashatz. 1. If he didn’t yet daven shemona esrei, or even if he did daven, but he forgot something which would cause him to have to daven again. For example, he forgot to say yaaleh vyavo, etc., then he should also say elokai nitzor. () 2. Someone else will be the chazzan from asrei uva l’ztion. Since then he will not be saying kaddish tiskabel, at least he should take three three steps back.
O:CH 123-5, M:B 123-18, 19, 20, Ketzos Hashulchan 22-11, Kaf hachayim 123-28.
See Pri Megadim E:A 123-13 that the words “tiskabel tzilosa’on” are the “elokei nitzor” of the chazoras hashatz. Therefore, when he is going to say it later in kaddish there is no point in his taking the three steps now. However, if he has to say elokai nitzor because of his own private shemona esrei, then he says elokai nitzor and takes the three steps back, and the and when he says tiskabel it will be the elokai ntzor of the tzibur.
When the chazzan didn’t daven before chazoras hashatz, regarding saying elokai nitzor, see Piskei Teshuvos 123-4 that it should be said unless it will cause the congregation to wait, i.e. they are not saying tachanun, or Rosh Chodesh when Hallel is started right away. In such a situation he should only say yihiyu l’ratzon, take three steps back and say ose shalom. However see Ishei Yisroel 24 ftnt. 155, and answers from Horav C. Kanievsky shlit”a 193 that our custom is that the chazzan doesn’t say elokai nitzor at all.