Perhaps SmartActions synonyms are what you are looking for:

http://help.k2.com/onlinehelp/k2blackpearl/icg/current/default.htm#Configure/IntCon_SA_Synonyms.htm

This is configured within the K2 server configuration file (K2HostServer.exe.config) located at<install drive>:Program Files (x86)K2 blackpearlHost ServerBin.  A restart of the service may be necessary after configuration changes.

Hello, 

I can't make it works.

I change the file K2HostServer.exe.config with from this 

<!-- Common configured actions and allowable alternatives -->
<!--
<action value="approve">
</action>
<action value="decline">
</action>

</actionsConfigured>

-->

to 

<!-- Common configured actions and allowable alternatives -->
<action value="approve">
<synonym value="approved"></synonym>
<synonym value="YES"></synonym>
<synonym value="OUI"></synonym>
<synonym value="OK"></synonym>
<synonym value="Validate"></synonym>
<synonym value="Approve"></synonym>
<synonym value="GO"></synonym>
</action>
<action value="decline">
<synonym value="declined"></synonym>
<synonym value="reject"></synonym>
<synonym value="rejected"></synonym>
<synonym value="NO"></synonym>
<synonym value="NON"></synonym>
<synonym value="KO"></synonym>
<synonym value="Refuse"></synonym>
<synonym value="NOGO"></synonym>

</action>

</actionsConfigured>

But this do not work in the mail , i receive the following mail : 

                  You may try one of the configured actions:
• Checked
• Reject

If i try to reply to YES or Approve or OK ... it doesn't work .. 'The K2 server did not understand your response for the worklist item.'

The mail only accept 'Checked or reject'

This value are the outcome of my workflow in K2 studio .. I have to add outcome for other way to reply ?

I restarded the K2 service and K2 machine.

Do you know the origin of the problem?

Thanks in advance,

I would like to confirm that in this task, an 'approve' action was configured/is available?

Additionally, could you try with self-closing tags:

<synonym value="approved" />

Intead of:

<synonym value="approved"></synonym>

To solve the problem, i checked the check box "Make this action available without opening the work item" in the K2 process on double click on action name