Do Stack Overflow managers have any thoughts on launching a Turkish version of the site?
There is an Area 51 proposal for it.
You can always commit to it (though, as it says on the page, is on hold while international features needed to make it functional are being added).
The Area 51 proposal referred on the other answer was deleted. Please checkout:
- Internationalization 'State of the Stack' - Stack Overflow edition
- Tl;Dr: Area51 stop receiving new site proposals for non-English sites.
- Changes to the Area 51 Process v3.0
- Tl;Dr: Proposals that doesn't meet the requirements for new sites were deleted. The major assumption is that the community exists before the new site proposal and that community is committed to timely complete the new site proposal process. Related: What makes a winning site proposal?