server {
    listen 80;
    server_name my.web.server;

    location ^~ /cdn {
        proxy_pass https://file.host/myfiles;
    }
}

my.web.server/cdn           => (proxy) file.host/myfiles/index.html
my.web.server/cdn/          => (proxy) file.host/myfiles/index.html
my.web.server/cdn/images    => (proxy) file.host/myfiles/images/index.html
my.web.server/cdn/images/   => (proxy) file.host/myfiles/images/index.html

my.web.server/cdn/**        => (proxy) file.host/myfiles/**/index.html
my.web.server/cdn/**/       => (proxy) file.host/myfiles/**/index.html

location ^~ /cdn {
    proxy_pass https://file.host/myfiles;
    try_files $uri $uri/ $uri/index.html;
}