Does Android support different resolution on external HDMI display from the built-in LCD?

Does Android support different resolution on external HDMI display from
the built-in LCD?

Suppose the Galaxy Nexus just supports 1280X720 resolution on built-in
LCD. When I connect an external HDMI displayer, can I output full-HD
1920X1080 video/overlay to the HDMI?
I know in the UI mode, the real resolution just is as same as the built-in
LCD. The content was stretched to 1920X1080. But it is possible to display
video stream on it as real Full-HD?
Thank you very much!