crontab need chmod?

[mobile.Parmenides]

I have installed cron written by Vixie Cron. After installing,
the crontab worked well as user root. But, when I switch to
another user named `work', there are some problems.

I have added the set-uid to the program /usr/bin/crontab and
made the directory /var/cron/tabs can be written and executed
by all users.

Then, when I executed the following command:
crontab workcron
in my $HOME( workcron is a crontab file in $HOME), I got the
a message like this:
chown: Operation not permitted
I don't have any idea of what relation is between chown and
crontab.

LFS 6.3 linux is my working system. The source code is available
in attachment.

[Lazydog]

What is the output of

ls -al workcron

What user is trying to execute the cron job?