personally I'd store the object in an object store rather than serialise memcache, APC even a session can be used, you can also use nosql style databases and key stores all of which are pretty much perfectly suited to object persistance as they're mostly very fast access data stores without the sql overhead. nosql-database.org
Just assign each object a key based off the key of the user browsing generate a new key for each new browser and store it in session/cookie to retrieve their personal "objects"
As already mentioned by STT you can serialise and store in the session thats perfectly fine although serialise is retarded to implement in php they should never have put that in.
Instead look at APC and SPL both are built in to php (APC is more suited for an object store especially since from 5.6 (I believe so onwards) its no longer an extension but built into the PHP core its self making it fully native so you get not only a simple object store but also op code cache which will seriously increase the speed of your php pages.
Note: APC is only really usable for object store when you run a single web / php server if you need multiple processing servers then you'll need a distributed object store in which case the best you can probably get is memcache
Lots of links mostly all on SO.
When should I use Memcache instead of Memcached?
Memcached vs APC which one should I choose?
http://php.net/manual/en/book.memcached.php
http://php.net/manual/en/book.apc.php
Is there a way in PHP to use persistent data as in Java EE? (sharing objects between PHP threads) without session nor cache/DB