Don't think there should be any problem with what you're suggesting. Gonzalo Figueroa (Argentine native, living in Norway), drove a Norwegian registered bike from Los Angeles to Buenos Aires. And Enric (Spanish native, living in USA) flew a US registered bike to Chile, then drove it back to USA.
So, the citizenship of the owner does not have to be the same as the country the bike is registered in. As long as you have all the paperwork to say you own the bike, you should be okay.
If you plan to bring it into Argentina and keep it there, of course you are legally required to pay import duties.
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