Why does the media keep saying Fiat bought out Chrysler?

When a "purchase" is made one party generally transfers money (or some other asset) to another party. As far as I can tell though, Fiat paid nothing for the good assets of Chrysler. The only thing anyone ever says is that Fiat is contributing the technology to make small cars to Chrysler. But since they own the company, that's like taking money out of one pocket and putting it into my other pocket. These companies are no longer separate entities, and Fiat is transferring these technologies not to "Old Chrysler", or to any of the stakeholders of "Old Chrysler" (ie Cerberus, the Federal Government, bondholders), but rather to "New Chrysler", which is a subsidiary of Fiat. So from my reckoning, that's not an actual transfer of assets outside of the company, and thus not a sale. So my question is, did Fiat actually pay anything for Chrysler? If not, why is it called a sale, and not a gift from the Federal Government?