IMO that is bad place for a stove the hood will block part of the window and just look wrong. I can’t tell if that is a gas range in which case the window would have to be inoperable to comply with code , why not vent out the wall if this is to code

Thanks for the feedback. The cooktop is induction. We were not going to swap the sink and cooktop. I have seen the exhaust hoods in front of Windows in pictures here on houzz and it does look quite nice. It currently does vent out as the question stated, venting out above and to the left of the ceiling beam (the black hose in the top left of the picture).

Where do you want the hood portion to sit? I don't know what the suggested is, and you probably do, so where would it be on the window?

(only because if we're thinking of the same thing, I'll try to remember where I saw it, if not I won't)

You might try a downdraft style exhaust system then you could vent low to outside through that wall. Most vent fan systems have specific requirements that limit elbows , turns in bent piping etc.

I agree with Flo. That seems to be the best option.

The downdraft may be the best option. We were trying to find something like this photo.

I've never seen one like that before. But it is wall mounted so it wouldn't work with your window. We have one mounted from the ceiling in front of a large window and it looks great. Seems like if you drop the ceiling you'd have room to worm around the beam. You can get a remote blower if you have to. But unless you do a lot of frying and grill panning you could get away with a ceiling exhaust fan.

What about this?

You can buy an offset vent adapter (it's for a stove) that would, essentially, give you the center vent for the stack then it would just be a case of a box to cover the adapter....might be worth looking into....your stack would be short, but it looks like it would be anyway...

I believe you can have 3(?) turns so you would be okay with that.

You might consider using a "under cabinet mount" unit. Your carpenter would build the "box" required to install same. Large HVAC dealers / installers would be able to modify the exhaust "outlet" to meet your existing vent.

There are no codes in the IRC restricting operable windows above cooktops, even gas. However, there are a few codes that says you can't vent the range hood through the wall above the window.

Also, that is a load bearing header above the window that you can NOT cut a hole in to vent through the wall.

Fred S that is correct- there is the header which is an additional hurdle.

They have exhaust fans that look like recessed lights. You could the fan light on the left and a matching nonfan light on the right.

I feel as if the outer casing of the stack of the hood I listed would accommodate this:

http://www.efireplacestore.com/sbi-ac01370.html

It's adjustable for various offset-ness...(sorry it's the only word I could think off!) but it' says it's less than three inches high.

kjbjw...That unit has a 90 degree turn...not recommended for stove venting (ok for fireplace "stove"). I think it has something to do with grease buildup.

Chiflipper 90 degree turns are fine.

@chiflipper,hood vent filter prevents grease particles from entering the duct, as long as your vent louvers open and operate properly when you turn on the fan, your fan will will do what is intended to do.

Like Fred said, you cannot drill through the header, but you can go above the header if ceiling joists are perpendicular to that wall or there is no obstructions... but if framing runs parallel to the wall or there is obstructions, this is why you use the soffit to conceal the duct and duct can go above the cabinets, etc, as I indicated in the picture above, you divert the duct and exit through the wall above the cabinet, this is even better, your Fan discharge is away from the window.

Here is another detailed image with a see through view.

Good luck

Here's what we ended up doing. The Jenn-air downdraft cooktop works pretty well.