Today I went to infopass and the IO is nice. He told me that GC checks include fingerprint, name check and internal check. The first two are done by FBI, the third one is done by CRIS. Name check is to check everything related to you which invloves over 20 agencies including IRS, bank, etc. Background check is one kind of check included in name check and it is the most time consuming one since FBI need to check your background in your home country. The internal check is just done by CRIS to make sure your previous status is OK which should be fast.
Hope this information is useful to all friends waiting for GC.