You can add a video slide to the home page slideshow that will automatically be resized to fit the entire content area. The video will also be resized to accommodate the device's screen size.
To embed a YouTube or Vimeo video into the home page slideshow, first go to the Online Store > Themes > Customize Theme > "Home Page - slideshow". You'll find this 'Video Embed Snippet' text box:
When viewing a video on YouTube, click on the Share button located under the video player. Then click on the Embed sub-link. You can now copy the Embed snippet and paste it into your Theme Settings. The video size settings do not matter, your video will automatically be resized to fit the slideshow.
When viewing a video on Vimeo, click on the Share button located on the actual video player in the right-hand corner. A pop-up box will appear that will allow you to copy the 'Embed' snippet. You can paste this snippet into your Theme Settings.
This feature was added to Mobilia 2.0 and Responsive 3.2. It is also standard in Retina 1.0. You can follow the upgrade instructions if necessary.