Several of these medium-sized, black flies were stationed on a prominent sunlit rock in the woods at this location. They appeared to be displaying--buzzing up into the air periodically, and also engaging in scuffles with each other. I'm therefore assuming they were males. The flies had a prominent red abdomen, only visible when they flew. (Estimated size corrected from 18 mm, to 13 mm 5/20/2012.)

I was quite curious to learn their identity, and to get a photo of the red abdomen, so I took one specimen and pinned it for detailed photos:



The other photo in this series shows the display site. This was such a characteristic habitat that I thought it deserved a photo so that others can look for this behavior.

Thanks for comments. Looks like a Xylota/Chalcosyrphus.
There's a Xylota bicolor in the Georgetown University collection. Coloration looks similar, given some fading and they note damage from a trap.

Syrphidae of Oklahoma keys X. bicolor:

Metasternum pubescent 2

2. Third abdominal segment wholly dull orange, the sides rarely slightly darkened; arista bare-->X. bicolor

Their Description:
START QUOTE
Xylota bicolor Loew
Characteristics: Large, fairly robust species; length, about 13 mm; antennae large, black, noticeably longer than width of front in female; arista yellowish, darkened on outer half, longer than width of face; metathoracic spiracle distinctly smaller than third antennal segment; metasternum pubescent; anterior cross-vein joining discal cell at middle; anterior basitarsi of male without long hairs or black spines on ventral side, hind trochanters of male without spurs; abdomen, except first tergite, reddish-orange; male genitalia entirely reddish-orange; surstyli but little longer than broad.
END QUOTE

Length looks good--13 mm, just what I measured. I've got photos of the ventral surface as well. North Carolina State University has 7 pinned, but several others in that genus. X. bicolor is mentioned in Brimley (1), p. 354, from Raleigh, May-June.

Robin McLeod, in comments to the photo of pinned specimen, points out close resemblance to European C. piger/pigra, which is also reported from Canada. That appears to be what this is...