I am creating a Cortana skill on the Cortana canvas, I have a button. I wanted to know if it possible to have an 'imback' type of button to open a webpage.
You can supply an openUrl to a card action, or even use ChannelData to send a LaunchUri command, deep linking to an application. (I haven't tried this, but I assume 'http://websitename.com' will launch in the Cortana host platform's default browser.)
activity.ChannelData = new {
action = new { type = "LaunchUri", uri = "http://websitename.com"}
};