Final answer:
The Mongols chose Kublai Khan, the grandson of Genghis Khan, as their new ruler in 1260. He established the Yuan dynasty and moved the capital to Beijing.
Step-by-step explanation:
In 1260, the Mongols elected the grandson of Genghis Khan, who was known as Kublai Khan, as their new ruler. Kublai Khan became a powerful ruler and continued to have a significant impact on the Mongol Empire's trajectory. Although his ascendancy to power signaled political shifts and the beginning of the empire's fragmentation, he managed to establish the Yuan dynasty in China and move his capital to Beijing. Despite numerous challenges, including internal strife and the unwieldy size of the empire, Kublai Khan's legacy is still remembered for the influence he had over one of the largest contiguous empires in history.