I think you should work this through an Italian intellectual property lawyer who will consult an immigration attorney here in the US. I will add immigration to the practice area so an immigration attorney can give you some tips regarding the F1 status of your US agent.
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You can't as a student. The only possibility is an E-1 or E-2 visa, which requires a "substantial investment," generally an amount over $100,000 USD. The other question is why do you need this one person to do it? You can hire a US citizen or LPR.
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I think it might be helpful to discuss your plans over with a lawyer in more detail. As noted by immigration counsel, you need to consider the legality of your visa. You would not be able to participate in this while on a student visa.
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Contact Attorney Charles Doland [ http://www.avvo.com/attorneys/90025-ca-michael-doland-167000/website.html ]. If I remember correctly he now only speaks Italian but has significant experience representing Italian companies. Good luck.
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