Final answer:
The sternocleidomastoid is the muscle that originates on the manubrium of the sternum and is responsible for rotating the head to the opposite side.
Step-by-step explanation:
The muscle which has an origin on the manubrium of the sternum and rotates the head to the opposite side is the sternocleidomastoid. This major neck muscle is responsible for laterally flexing and rotating the head. When the sternocleidomastoid muscles contract unilaterally, they result in the rotation of the head to the opposite side. When they act bilaterally, they contribute to flexing the head forward. They are innervated by the accessory nerve, which controls these movements, making them an integral part of the musculature of the neck.