A major method by which material gets delivered to the Colorado River in the Grand Canyon is:

Solifluction

Explanation:

Solifluction involves the movement of soil particles or other materials which has been exposed to water down a slope. This process is common in areas with water bodies and a steep slope.

A major method by which material gets delivered to the Colorado River in the Grand Canyon is through the solifluction process as a result of the presence of water and steep slope.