Actually, I think Yamaha has dropped this capability in some of its later receivers.
You should be able to connect component video directly from the cable box to the TV for just watching the picture and coonect HDMI from the cable box to your receiver for general use. Then just select the video input you want on the TV. When you want to watch football, just select the component output on the TV and use the receiver to play whatever music you want. When you want to watch general TV or any other source from the receiver, select HDMI on the TV. You may have to push a few buttons on the remotes to select the right picture, but it is pretty easy to do. I am assuming your cable box can output both HDMI and component. Most do.
You should be able to connect component video directly from the cable box to the TV for just watching the picture and coonect HDMI from the cable box to your receiver for general use. Then just select the video input you want on the TV. When you want to watch football, just select the component output on the TV and use the receiver to play whatever music you want. When you want to watch general TV or any other source from the receiver, select HDMI on the TV. You may have to push a few buttons on the remotes to select the right picture, but it is pretty easy to do. I am assuming your cable box can output both HDMI and component. Most do.