Would I have a problem going back to the US if I have been out of the US for a year now?

Permanent Resident status is intended for people who actually reside in the U.S. With just a small number of exceptions, a single absence from the U.S. for a year or longer will give rise to a determination that the person has abandoned his/her residence in the U.S. and his/her status as a Permanent Resident. When that happens it can become necessary for the foreign national to commence the application all over again to gain permanent resident status.