Air freight or some other freight channel. But, if you are talking about standard passenger checked luggage, I do not know of any carrier which will either send international luggage separately from the passenger in voluntary situations or which will check across even connections, let alone separate tickets of more than a few hours let alone a week.

Air freight can get quite expensive and can also involve a lot of paperwork. Consider the hassle factor vs. the hassle of an extra bag.

If you post the carriers, the exact routing and so forth, you can obtain more accurate information here.