>go leave the artefacts in the woods some where and then give the authorities the GPS coordinates.
Or don't. Who's going to stop you after you get the money? You still have the jewels you can still sell them, or put them in your own private collection.
That's why police don't usually comply with criminal demands for ransom; criminals don't obey the law in the first place, why would they be expected to hold up their end of a deal?
If there really isn't a market, then keeping them could only bring trouble if you're ever found with them. Maybe you really do care about the cultural value of them, but also want to get rich in the meanwhile.
Or sell bit-by-bit. With 50% before and 50% after the good are "delivered". Thereby building some level of trust and allowing the buyer not to take too much risk at once.
Or don't. Who's going to stop you after you get the money? You still have the jewels you can still sell them, or put them in your own private collection.
That's why police don't usually comply with criminal demands for ransom; criminals don't obey the law in the first place, why would they be expected to hold up their end of a deal?