When you say "when I am connected directly," do you mean when you don't go through K2 workspace?

 And is K2 workspace hosted on a different server from forms services?

 And is your symptom that you keep getting or get prompted for login credentials but fail even after putting in correct ones?

 If so your Kerberos configuration is not set up properly.  You can log directly in a single-hop from your client PC to either server, but when the workspace server tries to authenticate with a second-hop over to the InfoPath Forms Services server where the form is hosted, it fails because Kerberos isn't working right.

This is only if the above listed questions are answered "yes," though, otherwise the problem is something else.

I changed the identity of the k2 blackpoint application pool to predefined network service. This solved the problem with opening the infopath based workflow tasked.
But this setting affects that it isn't possible to start and participate in k2 processes with sharepoint workflow integration.

I've encountered the same problem in our environment whereby tasks cannot be opened as we get prompts for credentials when hitting the k2 Web Services. Kerberos should not be an issue, as we're working within NTLM, and the K2 server and Sharepoint server are co-located on the same box.

 I suspect that there may be a problem (as you suggested Jochen) with the application pool identity accounts used (and their permissions).

Can someone advise what app pool accounts are needed, what they should be applied to, and what permissions they need? (I'd prefer to not switch to 'network service' if it causes K2 to break in other places.