But this Fitz is not the magnificent Robbie Coltrane, but an American, Robert Pastorelli, and this Cracker has been made specially for sale in the United States. He is still rumpled. His motto is still "Physician heal thyself - Not", but somehow he lacks the charm that made Fitz, with his many, many flaws, bearable in Britain.
Today Granada will find out whether the hour-long pilot has fired the imaginations of the executives who commission drama series for the American network ABC. A green light to Granada would probably mean a 13-part series with the hour-long pilot shown as the first half of a two-part special.
If it is a success, it will help pave the way for Granada's fully-fledged entry into the American television market - last week the production company indelibly associated with Manchester opened a US production company in Los Angeles. And Granada already has two other pilot ideas at ABC and a possible movie deal with the Fox network.
Classy British police shows - Prime Suspect, for example, and Cracker - along with costume dramas, documentaries and comedies have done fantastically well on American television, albeit on cable stations or the public broadcasting channel PBS. We have also sold numerous comedy formats to be re-made across the Atlantic according to American sensibilities - Absolutely Fabulous is apparently a casualty, however, its gloriously bad behaviour deemed just too naughty for the US.
But the Cracker pilot is a first: no British or US company has re-shot its own show for a foreign audience. Drama shows, says Gub Neal, the man who gave Jimmy McGovern the idea for the original Cracker, cannot be sold off as formats: somehow the success of a drama series is bound up with its creators.
Mr Neal is executive producer of the American version, which is shot in Los Angeles with an entirely new cast and a storyline taken from the British series. "The cultural context in which the central character operates is obviously very different," he says - in other words, Fitz drinks less, carries a cigarette but never lights it and hosts a radio phone-in show.
"He's still a maverick, he's still confrontational, he's still nihilistic, he's still troubled but his central energy is, I think, in some sense less ironic and less dour," Mr Neal says. "He's more optimistic, and he is more romantic in his aspirations and beliefs. The American Fitz really believes things may be put right, and I think Jimmy's character never believed that, he was living in a much darker and irredeemable world."
Ironically, however, while the American Fitz is younger and better-looking (in conventional terms) than podgy Robbie Coltrane, he is less interesting, less attractive and notable mostly for his intense charmlessness. I'd rather be treated by Frasier and seduced by the old Fitz.
The pilot has the unfortunate effect of making (comparatively) sympathetic the police officers who have to work with Fitz. In the American version, the racist, sexist, rapist pig from Northern Ireland is re-made as an uptight black man. This is apparently a daring assault on political correctness, though Gub Neal has not decided yet whether the black guy will end up raping his female colleague, as his Irish counterpart did in the British series. But the role exposes the need to rewrite for a different culture.
An ABC executive has been quoted as saying that Fitz is the natural successor to Andy Sipowicz in NYPD Blue "in the television evolutionary chain of flawed, damaged protagonists". Booze plays a supporting role to both men, but it is inconceivable that the original Fitz would take the cliched AA route, as Sipowicz did.
The problem, as Gub Neal says, is that "drinking in America, in Los Angeles, has the same stigma attached to it as taking cocaine in England".
More important for the feel of the programme, feelings, desires, beliefs, everything, have to be articulated, because the American sense of communication "tends to be more literal". There is not much room for subtlety or suggestion on American television - in the Cracker pilot the sex killer's chosen soundtrack is "You Don't Have to Say You Love Me".
None the less, Mr Neal and others see the transatlantic gap narrowing, and there are certainly rich television pickings to be had in LA for Granada's new American arm. "It is selling programmes, ideas and writers that are not readily available in LA ... there is an exotic interest," Mr Neal says.
The American business is highly regulated, with network officials paying regular calls to the set and demanding a great deal of control - something Granada will be well-placed to refuse, if necessary, Mr Neal says. "The advantage we have is that unlike all the other businesses operating in LA we're not dependent on the US market."
I hope Granada wins its commission from ABC - British television drama can be fantastic, and the more dollars British production companies make, the more they will have to create new and interesting shows, the more risks they will be able to take.
And the US market, indeed the global television market, is expanding apace. "If we can't set up production initiatives in the States that are competitive globally," says Mr Neal, "the danger is that we'll be completely overrun."
With the advent in Britain of digital television, we too will be able to tap in to dozens of channels with hours of airtime to fill. More in America has normally meant worse, but in a world where the future might be Carlton, we should be cheering for Granada to take on, and take over, the world.