For the Wireless Display Adapter, it can project 4K resolution. Visit this link for the display adapter's specifications.
Can you point me to the spec where you find the 4K? The max resolution seems to be 1920x1080 ("Full HD"), but not even that is written in the "Technical Data Sheet": http://download.microsoft.com/download/6/B/7/6B7DEB46-6836-4B18-ADFB-B8441492515F/TDS\_WirelessDisplayAdapter\_V2.pdf
Please, Mircosoft, allow 1920x1200 (WUXGA), too! :-)