Setting up smarthost on exim. How to defeat the Unrouteable address error when sending to "your" domain?

Question

linux

Hello! I set up a mail relay from the server to the mail for the Yandex domain via exim. I achieved a strange thing: letters go to any external domain, but they don't want to go to "their own". In the logs at the same time:
2014-02-09 17:38:35 1WCUah-0007KE-BL <= [email protected] U=root P=local S=491
2014-02-09 17:38:35 1WCUah-0007KE- BL ** recip[email protected]: Unrouteable address
2014-02-09 17:38:35 1WCUah-0007KI-CA <= <> R=1WCUah-0007KE-BL U=Debian-exim P=local S=1303
2014- 02-09 17:38:35 1WCUah-0007KE-BL Completed
2014-02-09 17:38:35 1WCUah-0007KI-CA ** [email protected]: Unrouteable address
2014-02-09 17:38:35 1WCUah -0007KI-CA Frozen (delivery error message)
Didn't do any direct settings.
mail sent by SMARTHOST; received via SMTP or fetchmail
Type System Mail Name: empty
Type IP Addresses to listen on for incoming SMTP connections: 127.0.0.1 ; ::1
Other destinations for which mail: empty
Machines to relay mail for: empty
Type Machine handling outgoing mail for this host (smarthost): smtp.yandex.ru:587
Hide local mail name in outgoing mail: No
Keep number of DNS- queries minimal (Dial-on-Demand): No
Delivery method for local mail: mbox format in /var/mail/
split configuration into small files: No
The last time I did this kind of thing, the problem was the opposite. Letters inside the domain went, but outside - no. Then I just got into the config and in 5 minutes I intuitively understood where and what to add. Now the config has become ... unintuitive. Or am I getting old...
I look forward to all kinds of help from you, friends!

Answer 1

It was useful to copy the config for @kerman and solved the problem. In the routers section of the smarthost description, the default is domains = ! +local_domains
Accordingly, you need to do domains = +local_domains

Answer 2

it was necessary to select the satellite mode))
smarthost - this is when he keeps mail for his domain himself, and the rest - on smarthost
satellite - send all mail to smarthost