Скопируйте bitrix:sale.basket.basket в свое пространство.
В коде
$dbBasketItems = CSaleBasket::GetList(
array("NAME" => "ASC"),
array(
"FUSER_ID" => CSaleBasket::GetBasketUserID(),
"LID" => SITE_ID,
"ORDER_ID" => "NULL"
),
false,
false,
array("ID", "CALLBACK_FUNC", "MODULE", "PRODUCT_ID", "QUANTITY", "DELAY", "CAN_BUY", "CURRENCY")
);
Удалите "LID" => SITE_ID.