"Raised up" here is an idiom for "caused to live again" AT: "The God of our fathers caused Jesus to live again" (See: [[rc://en/ta/man/translate/figs-idiom]]),
Here Peter uses the word "tree" to refer to the cross which was made out of wood. AT: "by hanging him on a cross" (See: [[rc://en/ta/man/translate/figs-metonymy]])
# give repentance to Israel, and forgiveness of sins
The words "repentance" and "forgiveness" can be translated as verbs. AT: "give the people of Israel an opportunity to repent and have God forgive their sins" (See: [[rc://en/ta/man/translate/figs-abstractnouns]])
# Israel
The word "Israel" refers to the Jewish people. (See: [[rc://en/ta/man/translate/figs-metonymy]])