Peleg replaces Shay Tangi, who heads all retail activity in the Sagi Group and will now serve as Layam chairman.
H&M Group's & Other Stories will open outlets in Tel Aviv and Jerusalem in the fall.
Fox has signed an agreement with the Danish chain's owner Zebra for the exclusive franchise to operate the Flying Tiger stores and website in Israel.
The executives who were mistakenly paid bonuses due to an accounting error will fight the matter in the courts if necessary.
Zap Group is Israel's largest consumer website company, with more than 20 websites that have over 17 million monthly visitors.
"After I have accomplished the missions I set for myself, it is time for a new path."
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