21-year-old male / 21-year-old female girlfriend has a past with her male friend.

My girlfriend and I had been together for 10 months when she admitted to kissing a close friend of hers a few months prior to our relationship. She reassured me that she never had any romantic feelings for him, but it made me reconsider a previous instance when she mentioned wanting to buy something from him but ended up spending over an hour driving around with him, which struck me as odd at the time. Intrigued about their connection, I reviewed their text messages and found some unsettling exchanges. Before we started dating, she had invited him to spend the night, and at one point, they spoke frequently. She maintains that she never had feelings for him, regrets the kiss, and asserts that they never discussed it again. While I can't alter what occurred before we met, what frustrates me is that she continued to make an effort to see and spend time with him while we were together. I've already tried to end things twice because I view her actions as a form of cheating; it’s hard to believe a girl would invite a guy over for a sleepover without some underlying attraction. She became distressed, insisting she doesn't want to be seen that way and believes we can still make it work, but honestly, I feel foolish for sticking around. Should I break up with her because I see this as cheating, or should I stay and hope she proves that she won’t engage in this behavior anymore?