Thank you for your question! This response will cover two issues. First, I will cover whether foreign citizens can form LLCs in the U.S. Then, I will address whether you can work for the LLC. The United States has fifty different states all of which have different requirements for LLC registration. Oddly enough, however, there are no restrictions on foreign ownership of a LLC formed in the United States. The procedure for a foreign citizen to form a LLC in the United States is the same as for a US resident. And it is not necessary for a corporate founder to be a US citizen or to have a green card.
Ironically, though, the mere fact that you can found a corporation in the United States does not mean you can reside in the country and work for the firm. A foreign citizen may be a corporate officer and/or director, but may not work in the United States or receive a salary or compensation for services provided in the United States unless the foreign citizen has a work permit (either a green card or a special visa) issued by the United States. You can own a business but unless you have a work visa, you are not allowed to work for your company in the US (You can work for your company in your country). If you would prefer to have advice on selecting a worker visa so you could work for the company, message me for more details. I hope this helps.
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