The correct answer is option 1: Basavanna. Basavanna was the founder of the Virashaiva Movement in Karnataka. The Virashaiva Movement, also known as the Lingayat Movement, was a social and religious movement that emerged in the 12th century in Karnataka, India.

Option 2: Appar - Appar was a 7th-century Tamil poet and one of the 63 Nayanars, who were considered saints in the Shaiva tradition of Tamil Nadu. He is not associated with the Virashaiva Movement in Karnataka.

Option 3: Sambandar - Sambandar was another 7th-century Tamil poet and one of the 63 Nayanars. Like Appar, he is not connected to the Virashaiva Movement in Karnataka.

Option 4: Sundarar - Sundarar was a 9th-century Tamil poet and one of the 63 Nayanars. He also has no association with the Virashaiva Movement in Karnataka.

In conclusion, Basavanna was the founder of the Virashaiva Movement in Karnataka, making option 1 the correct answer.