Symptoms

Initial Issue:
The main question here is: who are the email escalation recipients if the box titled "Send E-Mail to participants" is checked?
Are these people the participants to the respective task, or the whole participants to a workflow - which can be hundreds of people? This feature is not covered anywhere in the tutorials, documentation, or the community articles.

Follow up issue:
What is the format I can save a workflow variable in to get a group stored in this variable so I can redirect a task to a group?
I need this procedure since task redirect escalations cannot be assigned to groups - which would be a good feature to add. So it looks like I have to save the target redirect group in a variable, and then drag it into an escalations windows from the Context Browser.
 

Diagnoses

Initial Issue Diagnosis:
If this box is selected it only is sending to the participants of that particular event.

Follow up Issue Diagnosis:
We can use a smartobject to pull in a sharepoint group to be used as destination users for the escalation. There is a "Group" smartobject under SharePoint 2013 -> ;Site Collection] -> Management. There is also a "Users and Groups" smartobject located under "Task Allocation" Category.
 

Resolution

Initial issue Resolution:
If that box is selected it sends the email to the participants to the respective task.

Follow up Issue Resolution:
We found a smartobject that would supply the necessary user name in order for us to assign destination users to a particular sharepoint group for an escalation. Specifically we found that if we used the Name property on the Users and Groups Smartobject we saw our escalation successfully send to all users in the test group we were using. This Users and Groups smartobject is located under the "Task Allocation" Category and we used the method of "Get Email for Group Users". Note that the main requirement here is that we need a smartobject to pull back users in a group that does not pull from the K2 Identity cache. This smartobject fulfills that.