Quote Originally Posted by Redleg
The Mexican-American War was fought and New Mexico, Arizona, California parts of Nevada, Utah, Colorado were ceded to the United States by Mexico as a result of the Peace Treaty. I also believe the United States might of made a cash payment to Mexico.
We did. A further purchase was made years later to facilitate a railroad (The Gadsen Purchase; last segment of land acquired to form the continental 48).

As to returning land to the "original" owners, it called to mind a little ditty I enjoy:

Give Ireland back to the Irish/
Give Lappland back to the Lapps/
Give China back to the Chinese/
...and Yoko back to the Japs/



(Note: Sons and daughters of Nippon, I would not seriously advocate anything so heinous.)