Everyone is thinking the same thing. Who is this guy? Is he any good? Will he deliver at Parkhead? Are Celtic taking a major risk here?
A few others might be thinking John Barnes. Others still might be thinking Paul Le Guen. Or Tony Mowbray. We've seen some lauded names come to the Glasgow football hothouse and fail abjectly at Celtic and Rangers. It happens.
What made this so-called "risk" even more unnerving for Celtic yesterday was the revelation from Neil Lennon that, in fact, Deila had originally been earmarked as his new assistant at Celtic Park - before Lennon abruptly jacked in his job.
In other words, Celtic's original strategy appears to have been that Deila would be a number two, with a view to grooming him over time to become manager. Which only begs the question: have Celtic been forced to fast-track Deila, and is he ready for it?
The risk from Celtic's point of view is obvious. Deila comes from a tiny club in Norway - Stromsgodset's budget is miniscule, based in their 7,500-seater stadium - and he is making a major leap into the firmament of Celtic Park.
Everything about it will be different for him: the pressure, the expectation, the media gaze, let alone the Old Firm's outlying lunacies. This is no ambient Nordic idyll. Deila is about to face Scottish football in the raw.
All that said, he has much going for him, and Celtic's boldness is to be commended. The club has mastered the art in recent years of sourcing gems of footballers and getting them ahead of their time - and making money. Now Celtic are applying the same tack to a seemingly very gifted young manager.
Deila has transformed Stromsgodset from a small, sleepy, inconsequential club, even by Norwegian standards, into cup winners and national champions. Not only that, but his success in Norway has been sustained, suggesting a deep conviction about his work.
Under Deila, Stromsgodset won the Norwegian Cup in 2010, were runners up in the league in 2012 and then won their championship last season. Nothing in football is guaranteed but there is the smack of a diligent, talented coach here who knows how to find success.
There seems little disputing Deila's substance as a manager. The key to him succeeding or not at Celtic lies in another area: his ability to adapt to new surroundings and take it all in his stride.
Le Guen couldn't do that in 2006 with Rangers. Nor could Mowbray in 2009 with Celtic. In fact players and managers by the score have failed - if I may exhume the old phrase - to "handle the Old Firm".
Ally McCoist, across Glasgow, once put it succinctly: "Everyone thinks it is easy, but it is not at all. Can you cope with being a Rangers or a Celtic player? Can you take the win-win pressure that comes with it?"
There will be no bedding-in period for Deila. He needs to make immediate progress with Celtic in Europe - and that means steering the club through Champions League qualifying rounds into the monied group-stage in two months' time.
There will be no sympathy shown to him for being young, relatively untried and new on the scene. Managers of Stromsgodset might get that luxury. Managers of Celtic do not.
This, I believe, will determine Ronny Deila's fate over the next few months, and maybe years. His bearing and self-belief as a coach in a foreign land will shape his destiny.