What do you think it could be?

What is the purpose of this investigation? You won't be able to prove anything. And what will be the result? If a person is innocent, you will label them a cheater. Will that be good? And if they are guilty, they won't care. Do you really think they will repent? They will just say they didn't cheat, and that's it. In short, here's an idea: play online only with those you trust, and you'll be happy. I also had suspicions of cheating at one time. I even almost stopped playing online because of it. But even if I'm 99% sure, as long as that 1% remains, I will never publicly reveal the name.