Web api 2 when publishing to iis returns error OPTIONS 404 not found?

Question

IIS

On web api 2, I wrote a service that I access via a post request with ajax. The request is cross-domain. So on iis express, on iis which is installed on my machine and on iis which I installed on windows 2008 r2 server, everything works fine. But as soon as I upload it to the hosting, I get an OPTIONS 404 not found error. I suspect IIS settings but which ones? I checked the request filtering (the "HTTP commands" tab) - it's clean there. Where to dig? The third day I suffer.