Claiming to be an extraterrestrial from a planet called 'K-PAX' about one thousand light years away in the Lyra constellation, Prot (rhyming with the word "goat", played by Kevin Spacey) is committed to the Psychiatric Institute of Manhattan where psychiatrist Mark Powell (Jeff Bridges) begins to evaluate him as a delusional. However, Prot's unwavering ability to provide cogent answers to questions about himself, K-PAX, and its civilization leads Dr. Powell to introduce him to a group of astrophysicists, where Prot claims to have journeyed to Earth by means of "light-travel" and goes on to display rare knowledge that resolves a puzzle for them.
After Prot explains that his people do not live in families, Dr. Powell invites Prot to his home for a July fourth picnic. Prot translates for the dog, eats, learns about Dr. Powell's family problems, and plays with the children until the sprinkler turns on and he freaks out.
Prot exhibits considerable influence over the other patients at the Institute, each of whom believes unquestioningly that he is indeed from K-PAX. Prot has explained that he can take one person with him when he returns; thereafter most of the patients at the institute ask to be taken to K-PAX.
Upon learning that many of his patients expect to leave Earth on July 27, Dr. Powell confronts Prot, who explains that it is a predetermined date. However, Powell believes this to be a significant date in Prot's life, a day on which he suffered a severe psychological trauma. Powell then decides to subject Prot to regression hypnosis, which works well. Using information gained from these sessions, Powell figures out that Prot is actually Robert Porter, a man presumed dead since attempting suicide after his wife and daughter were murdered in 1996.
On July 27, what is thought to be Prot is found lying catatonic under his bed, and one of the other patients is also missing. The missing patient is never found, and Prot does not return. The other patients do not recognize Robert as he is being wheeled out of the room.