Ansible yum module already provides a solution for this problem. The path to the local rpm file on the server can be passed to the name parameter.

From the Ansible yum module documentation:

You can also pass a url or a local path to a rpm file. To operate on several packages this can accept a comma separated list of packages or (as of 2.0) a list of packages.

The proper steps to do this would be something like this:

- name: Copy rpm file to server
  copy:
     src: package.rpm
     dest: /tmp/package.rpm

- name: Install package.
  yum:
     name: /tmp/package.rpm
     state: present

I think the best solution for this is as follows:

- name: Find all rpm files in /tmp folder
  ansible.builtin.find:
    paths: "/tmp"
    patterns: "*.rpm"
  register: rpm_files

- name: Setting rpm_list
  ansible.builtin.set_fact:
    rpm_list: "{{ rpm_files.files | map(attribute='path') | list}}"

- name: installing the rpm files
  ansible.builtin.yum:
    name: "{{ rpm_list }}"
    state: present

Looping through the files might cause Yum Lock issues. So this is better and efficient as we don't have to loop through all the files, instead we are passing a list of file paths to the yum module.

Foreword

You should never use loop or with_item with the yum module unless you have an extremely particular situation because (quoting the doc)

When used with a loop: each package will be processed individually, it is much more efficient to pass the list directly to the name option.

And do yourself a favor: adopt the modern full yaml syntax for calling modules. It's easier to read and linters (e.g. yamllint) will catch more errors earlier.

My example is following those two rules.

Core answer

None of your above tries are sending the actual list of files to the yum module with the absolute path for each element. This info is quite easy to retreive from your copy task if you register the result. You can then filter the data (with e.g. json_query) to get only the relevant info.

The below playbook should give you the keys to do the job

---
- name: Copy and install rpms
  hosts: all

  vars:
    RPM: 
      - gskcrypt64-8.0.50.86.linux.ppcle.rpm 
      - gskssl64-8.0.50.86.linux.ppcle.rpm 
      - TIVsm-API64.ppc64le.rpm 
      - TIVsm-BA.ppc64le.rpm

  tasks:

    - name: "Transfer Files"
      copy:
        src: "/root/ansible_playbooks/{{ item }}"
        dest: /root/
      loop: "{{ RPM }}"
      register: copied

    - name: "Install RPMs from local copied files"
      yum:
        name: "{{ copied | json_query('results[?!failed].dest[]') }}"

Notes

• The ?!failed filter in the query is only here to filter out results with an error if you ever decide to ignore errors on the copy task. You can remove it if you wish (i.e. json_query('results[].dest'))
• loop: "{{ RPM }}" is strictly equivalent to with_items: "{{ RPM }}". loop is a newer syntax and was introduced in ansible 2.5. Both syntax are valid. See ansible loops documentation for more details.

No, there is no simple way around coping the package to the remote host before installing. Ansible yum module expects a local file when you define a file in the name parameter.

IMHO it is not a good idea to keep packages inside the Ansible code base. Because they are binary and not exactly part of the actual Ansible code. It would be cleaner to setup a private repository and store those files there. That is the only way around coping a package in this situation I'm aware of.

The problem is you use the -i (inventory) flag without specifying an inventory path.

---
- hosts: "{{ host | default('all') }}"
  vars:
    remote_path: "{{ remotepath | default('/usr/local/bin') }}"
    rpm_package: "{{ package }}"
  tasks:
    - name: install rpm package
      yum:
        name: "{{ remote_path }}/{{ rpm_package }}"
        state: present

Run:

ansible-playbook pb-testyum1.yml -e "host=xxxdev01 remote_path=/usr/local/bin rpm_package=AvamarClient-linux-sles11-x86_64-18.2.100-134-RH7.rpm" --syntax-check

Though this works, I recommend that you use invetory file (-i) instead of passing your host via extra-vars