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@ElizabethHenning according to my reading of it, this answer is about the dangers of the idea that you can divide the world into "good" and "bad" people, and OP is asking for advice on how to do that (clearly, for OP the bad people are "bigots"). The McCarthy era is especially relevant here because back then, the discrimination was based on ideology, and to me it seems that discriminating for ideological reasons is precisely what the OP will end up doing if she pursues this idea.
@user106152 this answer is a word of warning, trying to make you aware of the possibility that your whole approach toward this issue might be flawed. Refusing to even consider theses points and instead responding with juvenile spite seems very unwise to me.
@cag51 That's not how I read the question. OP asks if he should report the cheating to the professor or go straight to the undergraduate chair with it, or do both simultaneously. The conversation they had before was originally on the weight of the homework grade and the hypothetical possibility of cheating on it, now that there is concrete evidence of cheating the professor should be informed imho.
Maybe there's another alternative: the OP's colleagues could send the author requests for a preprint of the paper. If the author says yes, then there's no harm done imho.
Why do you feel so strongly about "copying solutions off the internet"? What about copying solutions off a book, off a fellow student? I guess everyone does research on the internet if they can not solve a problem, do you consider that unethical? Where do you draw the line between drawing inspiration and "copying a solution"? Did the student claim at any time that it was their original work or did they just hand in some exercises they found on the internet?
