Father Kyle is Mass Effect's take on the eccentric cult leader, and servers most directly as a reference to Colonel Kurtz from "Apocalypse Now." Kyle leads a biotic commune on Presrop, and despite Alliance attempts to treat him for post-traumatic stress disorder suffered at the battle of Torfan, he has become unstable and dangerous. Here's how to complete his questline.
Father Kyle Mass Effect: Where to Find Major Kyle
Admiral Hackett assigns Commander Shepard the task of dealing with Father Kyle, though he leaves the means up to the player. When you arrive, you'll ultimately have two choices: negotiate with Kyle or break-in.
If your Shepard has the Ruthless background, Kyle will let you in right away. Once inside, you can choose to negotiate with Kyle to get him to surrender, or open fire. If you succeed in convincing him to surrender, he'll be taken for PTSD treatment and the cult will disband peacefully.
Kyle can be hard to find. In the building on the surface of Presrop, you'll find a switch in a back room that unlocks an underground facility. In the back of that building, you'll find Kyle himself.