For full WebDAV support in NGINX you need to turn on standard NGINX WebDAV module (providing partial WebDAV implementation) as well as this module for missing methods:
./configure --with-http_dav_module --add-module=<path-to-this-module>
location / {
dav_methods PUT DELETE MKCOL COPY MOVE;
dav_ext_methods PROPFIND OPTIONS;
root /var/root/;
}
cd /etc/yum.repos.d
sed -i '/\[epel\]/a exclude=nginx' epel.repo
wget http://yum.devopsx.com/devopsx.repo
yum install nginx