Troy and Britta's relationship has progressed, but they're trying to keep Abed in the dark. When Britta concocts an impressive plan to make it seem as if she didn't stay the night, Abed let's her know he's been aware of their fling all along, he was just playing the fool because she kept bringing breakfast over and he enjoyed the donuts.
At school, Jeff reluctantly agrees to join Abed on his road trip to the "Inspector Spacetime" convention. Seeing as he's not a booger-eater, Jeff won't be attending. Instead, he's going skiing with Annie nearby. Pierce wants in on the road trip, but both Jeff and Abed know how much of a buzzkill he'd be; they keep Pierce at bay by telling him they didn't invite Shirley either.
Troy and Abed are on cloud nine at the convention, but Britta's ignorance regarding the show is unbecoming to Abed. Jeff finds Annie wandering around the convention center and informs her an avalanche has killed a bunch of hikers at their ski destination. It's tragic news... they won't be able to ski today. Jeff figures they'd just go home, but Annie is so excited to be staying in a hotel without a number in its name that she wants to stay. Jeff leaves, but allows her to stay in his room if she likes. It's under his name.
Abed finally meets his pen pal Toby, a shady Englishman with a career in Nigerian banking, at the convention. The two hit it off right away, but Troy finds himself as the odd man out. Not wanting to be left out of the hijinks, Pierce and Shirley roll into the convention on their own. Failing miserably to blend in, they are instantly whisked away by two focus testers previewing the American version of "Inspector Spacetime." Pierce and Shirley represent some significant demographics.
The hotel staff thinks Annie is Jeff's wife. She eats up the fantasy and decides to play along. In the hotel lobby, a beautiful woman mistakes a leaving Jeff for Thoraxis, the super villain from "Inspector Spacetime." Sitting down, Jeff breaks out his best British accent and begins a conversation.
Back at the convention, a worried Troy is determined to not be replaced by the seedy Toby. His neurosis is only making things worse, though. Britta cheers him up by giving him a "cosmic spanner" and offering to take a souvenir photograph with him. Elsewhere, Shirley is frustrated when Pierce's overbearing personality begins to control the focus group conversation. His ideas are awful and no one else is getting a chance to rebut them.
The hotel staff has grown to love Annie, or as they see her, Mrs. Jeff. It's with a heavy heart that one of the bellman informs her Jeff is downstairs in the lobby "cheating" on Annie. When Annie finds Jeff flirting with the fan girl, she throws a drink in her face and causes a scene. The fan girl does the same, angry Jeff didn't tell her about a marriage he wasn't even aware of himself until five seconds ago.
When Abed is reluctant to join his new friend Toby at an upcoming convention in Europe, Toby begins to freak out and takes a psychotic approach to ensuring the survival of their budding friendship. Toby shoves Abed into a nearby prop phone booth and locks him in. Abed is nervous, but he's convinced Troy will find him and help him escape from his locked confines.
Troy's friendship sixth sense is tingling; Abed is in trouble. In a triumphant moment, Troy saves Abed from the phone booth and scares the clingy Toby off once and for all. Their friendship is restored. Back at the hotel, Jeff and Annie's friendship needs some restoring of its own. She apologizes for exploiting the hotel's confusion about their relationship. Jeff tells her, if they were actually married, he'd never cheat on her with some girl in a hotel bar. The two leave agreeing to finally hang out again after a day spent apart.
The study group reunites on the convention floor. Pierce and Shirley have made it out of their focus group in one piece, but the same cannot be said about the new direction of the Americanized "Inspector Spacetime." Jeff's had a change of heart about the convention, and in a moment of nerdy glory, he commands the attention of the entire room by screaming out the catchphrase of Thoraxis as he rips off his shirt. The entire building kneels before him. It has been a good day.