Specifically Tom Clancy’s Ghost Recon, which was released in 2002.
Here’s a portion of the plot summary from Wikipedia:
Ghost Recon puts the player in charge of a fictitious squad of U.S. Special Forces operators from Company D, 1st Battalion, 5th Special Forces Group (5th SFG) stationed at Fort Bragg, NC. Except for the “1st Battalion, 5th SFG” designation, this unit is entirely fictional. They are sometimes referred to as “The Ghosts”. Their role is not unlike other real world Special Operations Forces, in that their operations are kept highly classified.
Ghost Recon begins in April 16, 2008, with civil unrest in Russia. Ultra-nationalists have seized power in Moscow, with plans to rebuild the Iron Curtain. Their first step is clandestine support of rebel factions in Georgia and the Baltic States. This is where the Ghosts come in: to silence the rebellion. Armed with some of the most advanced weaponry in the world, the soldiers of the Ghost Recon force are covertly inserted into Eastern Europe and given specific missions to curtail the rebel actions and overthrow their benefactors.
The game’s storyline stems from political turmoil that came to light a few years earlier, in which the Ultra-nationalist regime came to power and placed its leader, Dmitri Arbatov, as Russia’s president. By 2007, the threat posed by the Arbatov Administration became clear. Russia forms an alliance called the Russian Democratic Union (RDU), which is made up of the previously conquered countries of Ukraine, Belarus, and Kazakhstan. Together, they launch a campaign to revive the long-dissolved Soviet Union by taking back all of the former Soviet republics.
During the first few missions of the game, the Ghosts battle South Ossetian rebel forces from the north of Georgia, who are harassing the legitimate government and its allies. The Ghosts fight in the forests, on farms, and in villages while assisting their NATO allies in fighting the enemy. The Russian government complains to the United Nations that the Americans have interfered in their affairs, and eventually they send in their army to aid the rebels. The U.S. cannot hope to stop the Russian Army from invading Georgia, so the Ghosts slow down the invading forces so that their allies can evacuate. Eventually, the Ghosts are all that’s left of the U.S. forces in Georgia, and they evacuate by SH-60 Seahawk helicopter on the rooftop of the American Embassy in T’bilisi, just barely avoiding the Russian forces. The Georgian government flees to Geneva and sets up a government-in-exile. With the fall of T’bilisi, Georgia surrenders and is forcefully incorporated into the RDU.