What does Peter accuse the nation of Israel of doing in Acts 2?
The nation of Israel is accused of having killed its Messiah, not by their own hands but by demanding it and causing Rome to carry it out, openly rejecting Him. They crucified the same Jesus whom God made Lord in Christ.
Les explains that Peter is only addressing the nation of Israel and remains on the same ground as before the crucifixion—the Abrahamic covenant and the other Old Testament covenants. In Acts 2:23, Peter says Jesus was delivered by the determinate counsel and foreknowledge of God, yet they took Him and by wicked hands crucified and slain Him. Les says Peter is accusing them of having killed their Messiah, even though they did not do it with their own hands: they demanded it and caused Rome to carry it out. Peter brings this to them because they openly rejected their Messiah. Then in verse 36, Peter says the whole house of Israel should know assuredly that God hath made this same Jesus, whom they crucified, Lord in Christ. Les notes Peter says nothing about a Gentile here. Killing Him did not stop God's program, because God raised Him from the dead and He is still alive. The message to Israel was to repent of rejecting their Messiah, and to prove repentance with baptism.
Him, being delivered by the determinate counsel and foreknowledge of God, ye have taken, and by wicked hands have crucified and slain: