Peter went with Cornelius' men back to Caesarea. Upon arriving he had to restrain and explain before he could proclaim.
Cornelius was NOT to worship Peter (nor should any man today). Peter was there, in violation of all ethnical customs, because God told him to go. Cornelius was primed and ready to hear all that God wanted to tell him: Peter was the voice.
Amazing truths emerged from Peter's Caesarean Message: God accepts men withtout regard to ethnicity, if the honor Him and walk with Him. Jesus set the example of a disciple's behavior: be active in one's community doing good and helping. God supports all who live for Him, forgiving sins and granting freedom in Christ.
The Gentiles entered Christ just like the Jews: all men are equal.