Nooooooo, please don’t do this. Your friend will give you a million reasons and excuses in the book as to why this is okay and legal but it is not. You will be held responsible for any debt the business incurs, you will be screwed over with your taxes, you will be the one that the law will go after for any lawsuits, etc. If your friend had good intentions, he would do all of this paperwork under his own identity. If he is in the country illegally and using that as a reason or an excuse, then one of his millionair friends can set up the business for him.
Side note: a good friend will not ask you to do something shady as such so please re-evaluate your friendship with this person. Are there feelings involved? Are you two more than just friends? Because even if there is some type of friends with benefit situation going on, you are not married to this person and they may be using you to get the business under your name.
Be your own cheerleader and don’t lose sight of what got you inspired to start your business in the first place.