I disagree. If that alien, subject to sovereign power of his homeland, commits a crime and is then apprehended, he is most certainly subject to the jurisdiction where the crime is committed....even if he protests such jurisdiction or did not intend to be come subject to it.
The relationship of the United States to an illegal alien who commits a crime is wholly dependent on our treaty obligations to the nation of the alien's citizenship. An alien has no rights here other than stipulated by treaty. This is why, likewise, a US consulate is often able to rescue an American from punishment in foreign lands where our citizens have inadvertently fallen afoul of the law.
There's money to be made translating this into Spanish!
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