Redirect to authentication server - Cookies are not forwarded


I’m running istio 1.6.1, and i created an envoy filter to the gateway to redirect traffic of non authenticated user to the IDP server (in my case keycloak). This first part is simple, and it works fine.
My problem is that after authentication succeeded, the user must be redirect to its original url he gave, but the cookies set during the authentication flow are not forwarded to the “redirect_url”.
AFAIK, the browser should do the job my itself.
Can you please confirm my expectation. Did i miss something ?