[snip] The Kushans were one of five branches of the Yuezhi confederation, a possibly Tocharian, Indo-European nomadic people who had migrated from the Tarim Basin and settled in ancient Bactria. They may also have been of Iranian origin. During the 1st and early 2nd centuries CE, the Kushans expanded across the northern parts of the Indian subcontinent at least as far as Saketa and Sarnath near Varanasi (Benares), where inscriptions have been found dating to the era of the Kushan emperor Kanishka, which began about 127 CE  Around 152 CE, Kanishka sent his armies north of the Karakoram mountains. They captured territories as far as Kashgar, Khotan and Yarkant, in the Tarim Basin of modern-day Xinjiang, China. A direct road from Gandhara to China was opened which remained under Kushan control for more than 100 years. The security offered by the Kushans encouraged travel across the Khunjerab Pass and facilitated the spread of Mahayana Buddhism to China. [/snip]
The Tocharians were the easternmost speakers of an Indo-European language in antiquity, inhabiting the Tarim basin in what is now Xinjiang Uyghur Autonomous Region, northwestern People's Republic of China. Their unique culture spanned from the 1st millennium BCE to the end of the 1st millennium CE. Their language is called Tocharian.
The Tarim mummies suggest that precursors of these easternmost speakers of an Indo-European language may have lived in the region of the Tarim Basin from around 1800 BCE until finally they were assimilated by Uyghur Turks in the 9th century CE.