Is it possible to swap 2.2 2007 HHR cylinder head onto a 2006 2.2 Cobalt ?

Believe so, check your casting part number on the head. I believe 2.2 2006 to 2010 works for HHR, Cobalt, and Malibu.

n 2007, the L61 received a multitude of changes, that originated from the LE5. It switched to the higher-strength Gen II block and received a revised cylinder head (enlarged exhaust ports) and camshaft design (increased exhaust valve duration). The engine also switched from wasted spark ignition to individual coil-on-plug ignition; this forced the cam cover to be redesigned. It was also switched to an E37 engine controller with new crank and cam sensors (replacing timing sensor previously found in ignition cassette). These changes increase horsepower slightly and allow the engine to meet PZEV standards.[10] Compression ratio is 10.0:1.