Getting a live TV feed is up to the user, but thanks to the expandability on the back of the Shield (two USB 3.0 ports), Nvidia demoed an external over-the-air HD tuner and antenna that plugged into the back.
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I think this is demoing what you asked, but we never got this feature as an update.
im sure it could. you would just need an app that connects to the usb tuner and serves the content to the TV input framework.
imagine an hd homerun app that uses a usb tuner instead of a network tuner.
Theoretically yes, the app merely sources content from the TV Input Framework.
Practically in terms of connecting a USB-based tuner to an existing device such as the Nexus Player, it might not work as there needs to be some kind of interoperability between the tuner itself and the TV Input Framework, which is likely not something you get out of the box.
But I think Sony's TV's work that way currently actually.