K-PAX

A series of Science Fiction novels written by Gene Brewer, who also narrates the books in the first person as the protagonist, H. G. Wells-style. The books follow "Dr. Brewer"'s experiences with prot [sic, rhymes with "oat"], a supposedly delusional yet extremely convincing mental patient who looks like an ordinary, affable man but claims to be an extraterrestrial from a planet called "K-PAX".

The series contains four novels to date: K-PAX, K-PAX II: On a Beam Of Light, K-PAX III: Worlds of prot, and K-PAX IV: A New Visitor from the Constellation Lyra.

The first novel was adapted into a film of the same name in 2001, starring Jeff Bridges as the psychiatrist and Kevin Spacey as prot.

Tropes used in K-PAX include:

Aliens Speaking English: prot claims that English is easy to learn, at least when compared to his native language.
All There in the Manual: Aside from the alternate perspective of prot's true identity between film and book, the book goes much more in depth on the backstories of the other patients and Brewer himself.
Crap Saccharine World: Brewer considers K-PAX to be one. prot describes it as a utopia with no violence or war, no hunger, no crime, no government or currency, no pollution, everyone is a vegetarian, and everyone is a scientific genius free to travel the universe as they wish. Brewer sees this as meaning they're essentially wandering nomads with no sense of love or family structure.
Crazy Consumption
Crazy Enough to Work: prot's methods to cure Howie. At first Brewer muses that it makes sense to encourage an obsessive compulsive to focus on specific tasks over a long period of time. Then prot tells Howie to cure Ernie of his fear of death, which he does by strangling him into unconsciousness and then reviving him, and it works. His final task for Howie is to be ready for anything prot might request of him, eventually leading Howie to realizing obsessing over knowing everything is futile.
Deadpan Snarker: prot in the film, snarky but not so deadpan in the novel

Dr. Powell "What would you say if I were to tell you that I don't think you took any trip at all, to Greenland or Iceland or anywhere? That I don't believe you're from K-PAX? I believe you're as human as I am?"
prot: "I would say you're in need of a thorazine drip, doctor."

Demoted to Extra: The other patients in the film.
Driven to Suicide: Robert Porter, but he fails and the prot personality takes over.
Humans Are Special: prot subtly slips into this in the film as he prepares to leave, where he tells Brewer that no one ever misses him on K-PAX when he leaves, but he senses he will be missed when he leaves Earth, and realizes he'll miss them too.
- Humans Are the Real Monsters: In the book however he notes humans are ignorant of the damage they do to themselves, their planet and other animals, and writes in his journal that unless a radical society shift takes place he doubts the species will survive.
Law of Alien Names: Averted. The (uncapitalized) "prot" is a vowel shorter than its pronunciation would imply.
Literary Agent Hypothesis
Maybe Magic, Maybe Mundane: The series and film revolve around the idea that prot could be alien or human, there's good evidence for both.
Meaningful Name: "prot" is derived from Porter, Robert's last name.
Human Aliens: Subverted. See Starfish Aliens entry below.
Schrödinger's Gun: The film and book both take different stances on their evidence that prot is human or alien. The book contains more in-depth hypnosis sessions that have the Robert Porter personality come out and speak to Brewer, and flashbacks show a gradual growth in the detail of the world of K-PAX as he creates it in his mind, giving strong evidence that prot is just a split personality. The film leaves these two points out and has a greater focus on prot's inexplicable abilities, and twice when he would be "arriving" from his faster-than-light travel there's a glare of light and a quick cut away before he appears seemingly out of nowhere, giving a stronger implication that he's an alien.
Starfish Aliens: Subverted. prot claims that K-PAXians are this on their home planet, but look like the most efficient creature of the places they visit. It turns out that there's a bit more to it than that.
The Stoic: prot in the film is universally calm and collected. Not so in the novel.
Through the Eyes of Madness: When prot "leaves" in the end, the other patients comment that Robert Porter looks nothing like prot, implying they could see him for what he is.