Is my boyfriend seeing his ex-wife?

My boyfriend and I have been together for almost 2 years. He has been divorce for about the same amount of time. He recently started wearing his wedding ring on his middle finger. When I asked him about it he said it just looked nice. I also saw text messages and phone calls from his ex wife in his phone. We have broken up before due to the fact I had reason to believe he was still seeing his ex wife. He has lied on numerous occasions, lies he will not admit to. He said he does not want to be with her at all and he wants to one day marry me. I have invested so much into this relationship, but I am willing to let it go if I have to. I have no tangible evidence of him cheating. What should I do?