You will need an ATSC over the air digital tuner with HDMI output. Connect that to one HDMI input.
Connect the Roku to the other HDMI input.
The monitor has to be HDCP compliant for this to work with either source.
I hope I am replying to americanaudiophile. My initial query was incomplete. Your solution was fine as far as it went. My problem is my ASUS monitor. The only way to switch between HDMI inputs is by means of menus accessed by buttons underneath the bottom of the screen. Very tedious. Volume also and the volume is pathetic. What I want is a tuner, if possible, with a cable input from my antenna and an HDMI input from my ROKU stick, an HDMI output from the tuner to my monitor, and the ability to switch between inputs by means of a remote. It would be helpful if the tuner also allowed me to control volume as well. Is there a single tuner that would let me accomplish this or is there a dual tuner solution? Thanks.
Then you want a tuner with HDMI switching capability, see one with multiple HDMI ports? that's it. I personally don't have experience in availability. U maybe able to buy a switcher as a separate box, so Tuner ---> Switcher ----> TV.
What you doing for sound? (thinking one step ahead) 'cuz an AVR is a switcher as well as some soundbars.