I grew up listening to Oscar. Saw him three times in concert, as a soloist and in a band, once on a show where he and Ella Fitzgerald had Ray Brown, Bobby Durham and Joe Pass as the band. He's the reason why I decided to become an improvising musician.
One thing I advocate in my lessons is tapping the
left foot to keep time. Watch the Oscar Peterson video, His left foot is always going when he's playing a groove.
This gives each hand something to relate to besides the other hand, and gets your body involved in music-making. Playing with only your digits will never have the groove that body involvement will give you.
The left foot is important because, for a pianist like Oscar, the left hand is the time-keeper in the music. This is true for most Stick players as well.
For more on the importance of tapping your left foot, please see:
http://www.greghoward.com/free_hands/dvd/