Drupal commerce WPS , if user not go back to the site after paypal payment? this is the problem.
The payment used in my site is WPS (With Paypal Business account) so user switch from my site to Paypal site to pay order in cart. 

BUT

If User close paypal site after paypal message "Payment complete" and NOT go back in site, the status order stay on "Checkout: Complete". Drupal Commerce has no way of knowing that payment is complete so not send order email and decrease stock.

Is there a way to get around this problem?

I work with drupal commerce kickstart 2 (+ stock module)

Ty for your reply :)
I was experiencing a similar problem - no confirmation emails etc.  

Apparently what was causing the problem for me was that I had created a custom Rule that fired "When an ordered is first paid in full"  and updated the order status to "Completed." This custom Rule triggered after the user used PayPal WPS to complete payment. I did this to avoid the confusion of having the default status "Pending" after the the PayPal payment was successful.  

For some reason, having this custom Rule there prevented all the Rules that use the trigger "Completing the checkout process" to trigger (these default rules include all the notification emails among other things).

See this posting here for a few cases of other people who ran into this problem: https://drupalcommerce.org/discussions/1150/resolved-completing-checkout-process-not-firing

This issue was resolved (in my case) by just getting rid of the custom Rule. 

I'm wondering if this is causing the problem for you too.