God gave the Gentiles repentance, Acts 11:18

When God gave the Holy Spirit to the Gentiles in Cornelius' house, what this showed the Jewish believers was that God had given them repentance leading to life.

Acts 11:18 is a verse—the first in our survey of “repentance” verses in the New Testament—in which a word derived from the verb metanoeō may arguably mean only a change of belief, without implying a change of behavior. The context is this: Prior to the events of Acts 10, the Church of Jesus Christ was strictly Jewish and Samaritan (after the events of Acts 8); Gentiles were not welcome. In Acts 10:1-6, Cornelius, a Gentile, the Roman centurion in Caesarea, had a vision to send for Peter. Peter, through a vision of his own (Acts 10:9-21) was shown that he was not to treat as unclean people God had made clean, and that he should go when Cornelius’ messengers arrived. Peter went to Cornelius’ house, and preached Jesus to them. Acts 10:34-43. However, while he was still speaking, “the Holy Spirit came on all who heard the message.” Acts 10:44. Because Peter and the Jewish believers with him plainly saw that the group of Gentiles in Cornelius’ house had received the Holy Spirit (Acts 10:45-47), Peter ordered that they be baptized. Acts 10:48.

Upon Peter’s return to Jerusalem, the other Apostles and the Jewish believers there questioned him. Their objection was not that he had Cornelius’ household baptized, but that he had gone to his house at all. “You went into the house of uncircumcised men and ate with them.” Acts 11:3. It was thought that he should not have associated with Gentiles at all. Peter then explained his vision, and Cornelius’ corresponding vision to send for him (Acts 11:4-14), and then describes for the brethren in Jerusalem the outcome of his visit to Cornelius’ household:

As I began to speak, the Holy Spirit fell on them, even as on us at the beginning. I remembered the word of the Lord, how he said, ‘John indeed baptized in water, but you will be baptized in the Holy Spirit.’ If then God gave to them the same gift as us, when we believed in the Lord Jesus Christ, who was I, that I could withstand God?” When they heard these things, they held their peace, and glorified God, saying, “Then God has also granted to the Gentiles repentance (metanoian) to life!”

Acts 11:15-18 (WEB)

Nothing in this context indicates that anything more than a change in belief is in view. But it was a change in belief to which God responded by placing his Holy Spirit on them!

Next: Paul’s sermon at Pisidian Antioch places repentance in John the Baptist’s message, Acts 13:24