Symptoms

When executing a SmartObject linked to the "SharePoint Service V2" Service Instance, there are constant 401 errors. Note this is done on a SharePoint 2010 server.
 

Diagnoses

It seems like Kerberos has been setup between the K2 and SharePoint 2010 servers. However when running the K2 Configuration Analysis Tool (from Start Menu), there is always an error under "K2 Windows Token Service".
 

Resolution

Please use this site to configure Kerberos correctly between K2 and SP2010:

http://www.astaticstate.com/2009/04/k2-blackpearl-kerberos-configuration.html

Since 4.6.8, the K2 Claims to Windows Token Service has been implemented, and this also needs its own configuration. Please refer to this KB article:

http://help.k2.com/kb001607 (make sure it looks exactly like the picture - it's important to have constrained delegation setup)

You can also read up a bit here:

http://mikerodionov.com/tag/k2-windows-token-service/