This question was answered excellently by the third response at the following link: http://www.avvo.com/legal-answers/if-a-couple-breaks-up-before-wedding-who-is-the-ri-6971.html .
Generally, unless there's some real clear facts indicating that the ring was given upon the condition of marriage, bad behavior by the donor would make it unlikely that a court would order the donee to give the ring back.
As far as whether the cheating you reference is sufficient bad behavior to alter the donee's entitlement to the return of the ring, that's a fact dependent issue. I don't think that's a question you can get an answer to on-line.
Talk to an attorney.