You probably have a “Norman” in your life.

He’s the guy who sends you follow-up emails to his follow-up email about his original email. When you see him in a crowded room, you try to make yourself invisible — but of course he makes a beeline for you and corners you to tell you about this incredible-amazing-fantastic deal he’s working on, and he’s going to introduce you to some very important people, and can he call you tomorrow with the details? If you would please just do him the honor of allowing him to do this favor for you, it would mean the world to him.

Richard Gere is the title character in “Norman: The Moderate Rise and Tragic Fall of a New York Fixer,” and it’s a tribute to Gere’s veteran skill set that we find the often irritating Norman also to be a fascinating enigma and on some level a truly sympathetic figure.

He makes us cringe, but we’re kinda rooting for him.

Gere delivers one of the most impressive and nuanced performances of his career as Norman Oppenheimer, a Manhattan consultant of sorts who is well into his 60s but still seems to be hustling for his first major break.

Norman’s the kind of guy who is forever “accidentally” bumping into movers and shakers on the street or showing up at events and working the room after wrangling invites under dubious circumstances. He’s always placing himself in embarrassing situations and almost forcing people to push him away, but he seems incapable of humiliation.

(In one perfectly choreographed scene, a wealthy power broker played by Josh Charles is hosting a party at his home and isn’t entirely clear how Norman got in. He quietly and ruthlessly dispatches Norman into the night with a tight smile and an icy look.)

Norman operates on the fringes of Jewish power circles, working every angle to finally get that seat at the table. He’s not without a certain amount of warm charm, which he uses to ingratiate himself with an Israeli politician, Micha Eshel (Lior Ashkenazi in a wonderful performance), who takes a liking to Norman even though his top aide and his wife caution him about Norman’s ulterior motives.

Cut to a few years later. When Micha becomes prime minster of Israel, there’s a celebration for him in New York. He welcomes Norman with a very public embrace and tells everyone in the room Norman is a dear friend and will be his most trusted confidante in the city.

Triumph! Victory! As Norman tells his nephew (Michael Sheen), “For once I bet on the right horse.”

(In one of the film’s myriad nifty touches, writer-director Joseph Cedar captures Norman’s moment by freezing everyone in the room except Norman, who is bursting with a combination of exuberance and disbelief. We get the sense this is the best moment of Norman’s life, and it might not ever get any better.)

“Norman” is populated by any number of intriguing supporting players, from Steve Buscemi’s rabbi to Charlotte Gainsbourgh’s government investigator to Harris Yulin’s influential power broker, who regards Norman with undisguised suspicion and openly wonders where this guy came from and what he’s up to. Even when Norman is riding his winning streak and taking advantage of his newfound status, there’s this uneasy aura stalking him, as if it’s all going to come crashing down at any moment.

Cedar engages in a number of cool visual touches, e.g., telephone conversations in which it appears as if the subject of Norman’s pitch is standing in the same room with him. (Although a few of the flourishes draw a little bit too much attention to themselves and distract from the dialogue at hand.)

More than 30 years after Richard Gere hit it huge with preening roles in films such as “American Gigolo” and “An Officer and a Gentleman,” he’s become one of the most interesting older lions in the business. Gere’s work in “Norman” is to be treasured. It’s one of the best performances in any movie this year.

★★★1⁄2

Sony Pictures Classics presents a film written and directed by Joseph Cedar. Rated R (for some language). Running time: 118 minutes. Opens Friday at local theaters.