I have a job in my home country. But I don´t have a job offer in the US. Actually, I want to keep my current job in my home country, even if I get a green card from the US. Is that possible?
Once your green card is approved, you have 6 months to come to the U.S. and claim it before it gets revoked. Once you are in the United States, you generally have to be present for at least 6 months within a given year. If you are gone longer than 6 months in a year, that can raise an issue with USCIS as to your intentions to remain a lawful permanent resident of the United States, and you may be barred from re-entering the country.
If your job in your home country will allow you to work remotely from the U.S., that will not be a problem. However, if you intend to remain in your home country, it may still be possible, but you will have to take extra steps to ensure that your green card will not be revoked.