I attempted to install SharePoint 2013 on Windows Server 2012 R2. It didn't go so well. The main problem is that you can’t install the SharePoint 2013 Prerequisites using the standard install wizard. It would fail every time it tried to configure IIS.
I did finally get it to work, but it was not trivial at all. Here is how to install the prerequisites manually.
INSTALL WINDOWS ROLES/FEATURES
You need to install the following roles and features:
DOWNLOAD AND INSTALL SHAREPOINT PREREQUISITES
Craig Lussier has written three scripts to download and install the SharePoint 2013 prerequisites, but only the download script works on Windows Server 2012 R2 (they probably work fine on vanilla 2012), because the install scripts use Prerequisiteinstaller.exe. So take advantage of the download script, and do the rest manually.
So the steps:
All the prerequisites should now be installed, and you should be able to install SharePoint 2013.