He lied so he should concede his seat
We would have at least 100 special elections if that were the criteria. Yes, I know that he's a total fraud, but democracy makes total frauds able to obtain public office.
As long as he votes the Republican line and doesn't derail Republican initiatives in Congress he'll be keeping faith with the people that voted for him (to the extent that this phrase can be used). Santos wasn't elected to be Newt Gingrich, but he WAS elected to vote the Republican line in Congress. He needs to do that to be fair to the voters that elected him.