Is She Cheating On Me?

I have not thought about her cheating, however one of my friends suggested it. Recently my girlfriend Lacey meet some Gentleman at her work named Forte. She seems to spend more time with him then me? I think they are just friends but my friend keeps on telling me that shes cheating. All she does is hang out with him. And has only spent the night at Forte's house. But I still take her shopping for whatever she wants. However She asked me if she could move in with Forte. Should I think she is cheating on me. Shes just going on a Jamaican Cruise with him as friends.