How do I eliminate the stroke added to pasted vector shape from illustrator to photoshop?

[JAbel]

Why is there a stroke on a shape when I copy from illustrator and paste in photoshop and how can I remove it in photoshop? 

[c.pfaffenbichler]

Could you please post screenshots with the pertinent Panels (Toolbar, Layers, Paths, Options Bar, …) visible and the Direct Selection Tool (A) selected? 

Is there a Stroke set in the Options Bar? 

[JAbel]

Sure thing. Here's the interface and a closeup with the grey stroke.

[c.pfaffenbichler]

Where is the Options Bar? 

And once again: Is there a Stroke set in the Options Bar?