B737NG Captain reported encountering wake turbulence on descent into DEN in trail of an A320.

Narrative

I was the CA/LCA on the flight. First leg of trip with new CA student. I was PF in the right seat; acting as F/O. On descent into DEN on LAWGR arrival. Turbulence was forecast for descent to DEN below FL200. Fasten seat belt sign was on and F/A were briefed about turbulence and completing their duties early. We were about 1 min from making PA for the FAs to take their jump seats. DEN Center had cleared us to descend via. Appropriate altitude set in MCP. Aircraft on autopilot; in LNAV and VNAV Path; 280KTS. In VMC and at approximately FL260; we experienced what we determined to be a wake turbulence event. The aircraft rolled left and then hard to the right. Amber caution on PFD and verbal caution 'Roll Authority'. I disengaged the autopilot; verbalized 'my aircraft' and hand flew roll recovery to stabilize the aircraft. Whole event lasted less than 5 sec (my estimate). With aircraft stabilized and continuing on lateral/vertical path; I re-engaged autopilot B. Other than the hard rolls; turbulence was nothing more than light; if even that. I asked the CA student to make PA announcement for F/A to take jump seats; which he did. Less than 5 sec after engaging Autopilot B; we had a 2nd wake turbulence event. Again; with hard rolls left and right; with 'Roll Authority' cautions. I disengaged autopilot; verbalized 'my aircraft'; and hand flew the aircraft until stabilized. Event lasted no more than 5 sec (my estimate). CA student notified ATC of wake event. ATC said we were following an A320. ATC then cleared us to slow to 250kts. With aircraft stable again; I re-engaged autopilot and then set 250kts in FMC descent page. A normal descent and landing were then accomplished with no further issues.