Maybe look for a more attractive design. I found this (don't know a thing about it) and don't know if it works for an exterior wall. Here is a link that might be useful: disappearing fan

Babka: ha. they (fixtures) are vented to the space above, (which is under the stairs), not to the outside - which is against the code, I know that much. I guess they (whoever added this bath) ran into the same problem with venting fixtures as we are facing trying to figure how to vent the exhaust fan. and maybe that's why there is no exhaust fan to start with. The bathroom is under the staircase whichi s in the middle of the house, and there is space directly above it because the ceiling is short. But then the ceiling height changes as you go to any neighboring room (the rest of the house around has much higher ceilings). Basically, you can put the duct vertically through the ceiling above the bathroom, but then as you turn it 90 degrees towards in the direction of any outside wall, it would have to come out through the wall of any room around, not in the ceiling above the rooms. And if you try to go higher with the duct so that the turn is at the level of the over-the-ceiling space for these rooms, then the duct would have to come out through the staircase! Hard to explain, but I hope you go the picture. Also, even if we could somehow get the duct to the space over the ceiling of any adjacent wall, then we still can't open up that high ceiling to run the duct further because it has some fancy beams and moldings (house is over 100years old) so we cannot touch the ceiling. That's why I wrote "absolutely no way" for the ceiling route Unless, as somebody above suggested, we place the fan in the ceiling, but run the duct through the wall down to under the house (actually through the under-the-stailrcase part as the stairs go down). But as far as I understand that comment, we will have to install some inline fans in the duct to keep the air moving down...

No attic access? No way to get up there at all? Not a ceiling scuttle hidden in a closet some where?Agree with Joe, we can give guidelines to install the fan, but the wiring is the issue. Do you have a plan for wiring the fan? Probably the easiest would be to extend the wiring from the bathroom ceiling light. Attic access would make it a heckuva lot easier. But barring any out of the ordinary attic framing, extending the ceiling light circuit could be done with a couple of fishing tapes. Is that an option? And then...there are wall exhaust fans. Again, depending on location, electrical would be an issue.

The installation of the bathroom exhaust is a big problem, but not your only problem. The overarching issue is that your kitchen exhaust is from the ceiling rather than a hood over the range/cooktop. Trying to work with an existing ceiling exhaust, even if you replace it with a correct ceiling exhaust, well, it's still a ceiling exhaust. Take this opportunity of your kitchen reno to improve this arrangement. Lots of problems with a ceiling exhaust, most notably: (1) too much opportunity for grease and smoke to escape to the rest of kitchen, (2) difficult to clean at the ceiling, (3) not enough cfms to pull the smoke and grease from such a distance, and (4) no canopy shape (as a hood would have) to corral the grease and smoke. Take the opportunity of your reno to install a correct hood exhaust. Edited to add: I just noticed you said you are in a condo. If you are stuck with that exhaust location, you can still install an "island hood" in a chimney style that meets the ceiling where the duct is located. Make sure the hood is in a canopy shape, and is 6" wider than the width of the cooktop.